भिन्न \( \frac{191}{5120} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{191}{5120} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.373046875)
B (0.0373046875)
C (0.00373046875)
D (0.1915120)
Explanation opens after your attempt
Correct Answer
B. (0.0373046875)
Step 1
Concept
\(5120\times1953125=10000000000\), so \( \frac{191}{5120}=0.0373046875 \). Converting a large denominator into a power of (10) is an exact method.
Step 2
Why this answer is correct
The correct answer is B. (0.0373046875). \(5120\times1953125=10000000000\), so \( \frac{191}{5120}=0.0373046875 \). Converting a large denominator into a power of (10) is an exact method.
Step 3
Exam Tip
\(5120\times1953125=10000000000\), इसलिए \( \frac{191}{5120}=0.0373046875 \) है। बड़े हर को (10) की घात में बदलना सटीक तरीका है।
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दशमलव (0.00025390625) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.00025390625) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{13}{5120} \)
B \( \frac{13}{51200} \)
C \( \frac{25390625}{1000000} \)
D \( \frac{1}{25390625} \)
Explanation opens after your attempt
Correct Answer
B. \( \frac{13}{51200} \)
Step 1
Concept
\(0.00025390625=\frac{25390625}{100000000000}=\frac{13}{51200}\). Count decimal places and write the fraction in simplest form.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{13}{51200} \). \(0.00025390625=\frac{25390625}{100000000000}=\frac{13}{51200}\). Count decimal places and write the fraction in simplest form.
Step 3
Exam Tip
\(0.00025390625=\frac{25390625}{100000000000}=\frac{13}{51200}\) है। दशमलव स्थान गिनकर भिन्न को सरल रूप में लिखें।
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यदि \( \frac{p}{q} \) सरल रूप में है और \(q=2^4\times5^3\times23\), तो दशमलव प्रसार कैसा होगा?
If \( \frac{p}{q} \) is in simplest form and \(q=2^4\times5^3\times23\), what type of decimal expansion will it have?
#number-systems
#decimal-representation
#prime-factor-test
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A सांत / Terminating
B असांत अनावर्ती / Non-terminating non-recurring
C असांत आवर्ती / Non-terminating recurring
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
C. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
The denominator has (23), a factor other than (2) and (5). So the rational number will have a non-terminating recurring decimal.
Step 2
Why this answer is correct
The correct answer is C. असांत आवर्ती / Non-terminating recurring. The denominator has (23), a factor other than (2) and (5). So the rational number will have a non-terminating recurring decimal.
Step 3
Exam Tip
हर में (23) है, जो (2) और (5) के अलावा गुणनखंड है। इसलिए परिमेय संख्या का दशमलव असांत आवर्ती होगा।
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भिन्न \( \frac{264}{440} \) को सरल करने के बाद दशमलव प्रसार कैसा होगा?
After simplifying \( \frac{264}{440} \), what type of decimal expansion will it have?
#number-systems
#decimal-representation
#simplest-form-test
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A असांत आवर्ती / Non-terminating recurring
B सांत / Terminating
C असांत अनावर्ती / Non-terminating non-recurring
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
B. सांत / Terminating
Step 1
Concept
\( \frac{264}{440}=\frac{3}{5} \), and the denominator has only (5). Therefore, its decimal expansion is terminating.
Step 2
Why this answer is correct
The correct answer is B. सांत / Terminating. \( \frac{264}{440}=\frac{3}{5} \), and the denominator has only (5). Therefore, its decimal expansion is terminating.
Step 3
Exam Tip
\( \frac{264}{440}=\frac{3}{5} \) और हर में केवल (5) है। इसलिए इसका दशमलव प्रसार सांत होगा।
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दशमलव \(0.670808080\ldots\) का सही बार संकेतन कौन-सा है?
Which is the correct bar notation of \(0.670808080\ldots\)?
#number-systems
#decimal-representation
#bar-notation
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A \(0.\overline{6708}\)
B \(0.670\overline{8}\)
C \(0.67\overline{08}\)
D \(0.6\overline{708}\)
Explanation opens after your attempt
Correct Answer
C. \(0.67\overline{08}\)
Step 1
Concept
After the first (67), the block (08) repeats. Put the bar only over the actual recurring part.
Step 2
Why this answer is correct
The correct answer is C. \(0.67\overline{08}\). After the first (67), the block (08) repeats. Put the bar only over the actual recurring part.
Step 3
Exam Tip
पहले (67) के बाद (08) का समूह दोहरता है। बार केवल वास्तविक आवर्ती भाग पर लगाएं।
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\(5.209\overline{36}\) को सामान्य दशमलव रूप में कैसे लिखेंगे?
How is \(5.209\overline{36}\) written in ordinary decimal form?
#number-systems
#decimal-representation
#bar-notation
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A \(5.209363636\ldots\)
B \(5.20936209\ldots\)
C (5.20936)
D \(5.20920936\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(5.209363636\ldots\)
Step 1
Concept
The bar is only over (36), so after (209), (36) repeats. The barred part repeats continuously.
Step 2
Why this answer is correct
The correct answer is A. \(5.209363636\ldots\). The bar is only over (36), so after (209), (36) repeats. The barred part repeats continuously.
Step 3
Exam Tip
बार केवल (36) पर है, इसलिए (209) के बाद (36) बार-बार आएगा। बार वाले भाग को लगातार दोहराते हैं।
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भिन्न \( \frac{59}{72} \) का दशमलव प्रसार कौन-सा है?
Which is the decimal expansion of \( \frac{59}{72} \)?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.819444\ldots\)
B \(0.597272\ldots\)
C \(0.827777\ldots\)
D \(0.725959\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(0.819444\ldots\)
Step 1
Concept
\(59\div72=0.819444\ldots\). In long division, identify repetition from recurring remainders.
Step 2
Why this answer is correct
The correct answer is A. \(0.819444\ldots\). \(59\div72=0.819444\ldots\). In long division, identify repetition from recurring remainders.
Step 3
Exam Tip
\(59\div72=0.819444\ldots\) होता है। लंबी भाग विधि में आवर्ती शेष से दोहराव पहचानें।
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(0.8189), \( \frac{9}{11} \), \(0.818\overline{1}\) में सबसे बड़ी संख्या कौन-सी है?
Among (0.8189), \( \frac{9}{11} \), and \(0.818\overline{1}\), which is the greatest number?
#number-systems
#decimal-representation
#compare-numbers
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A \( \frac{9}{11} \)
B (0.8189)
C \(0.818\overline{1}\)
D तीनों बराबर हैं / All three are equal
Explanation opens after your attempt
Correct Answer
B. (0.8189)
Step 1
Concept
\( \frac{9}{11}=0.818181\ldots \), which is less than (0.8189). View all numbers in decimal form for comparison.
Step 2
Why this answer is correct
The correct answer is B. (0.8189). \( \frac{9}{11}=0.818181\ldots \), which is less than (0.8189). View all numbers in decimal form for comparison.
Step 3
Exam Tip
\( \frac{9}{11}=0.818181\ldots \), जो (0.8189) से छोटा है। तुलना में सभी संख्याओं को दशमलव रूप में देखें।
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यदि (0.94a7>0.9467), तो अंक (a) का सबसे छोटा मान क्या हो सकता है?
If (0.94a7>0.9467), what can be the smallest value of digit (a)?
#number-systems
#decimal-representation
#digit-comparison
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A (5)
B (7)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The tenths and hundredths digits are equal, so the thousandths digit must satisfy (a>6). The smallest value is (7).
Step 2
Why this answer is correct
The correct answer is B. (7). The tenths and hundredths digits are equal, so the thousandths digit must satisfy (a>6). The smallest value is (7).
Step 3
Exam Tip
दसवें और सौवें स्थान समान हैं, इसलिए हजारवें स्थान पर (a>6) होना चाहिए। सबसे छोटा मान (7) है।
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भिन्न \( \frac{97}{2048} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{97}{2048} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.04736328125)
B (0.4736328125)
C (0.0972048)
D (0.004736328125)
Explanation opens after your attempt
Correct Answer
A. (0.04736328125)
Step 1
Concept
(2048) is a power of (2), so the decimal terminates and \( \frac{97}{2048}=0.04736328125 \). Convert a power-of-(2) denominator into a power of (10).
Step 2
Why this answer is correct
The correct answer is A. (0.04736328125). (2048) is a power of (2), so the decimal terminates and \( \frac{97}{2048}=0.04736328125 \). Convert a power-of-(2) denominator into a power of (10).
Step 3
Exam Tip
(2048) केवल (2) की घात है, इसलिए दशमलव सांत होगा और \( \frac{97}{2048}=0.04736328125 \) है। (2) की घात वाले हर को (10) की घात में बदलें।
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दशमलव (0.000546875) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.000546875) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{7}{12800} \)
B \( \frac{7}{1280} \)
C \( \frac{546875}{1000000} \)
D \( \frac{1}{546875} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{7}{12800} \)
Step 1
Concept
\(0.000546875=\frac{546875}{1000000000}=\frac{7}{12800}\). Always write the final answer in simplest form.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{7}{12800} \). \(0.000546875=\frac{546875}{1000000000}=\frac{7}{12800}\). Always write the final answer in simplest form.
Step 3
Exam Tip
\(0.000546875=\frac{546875}{1000000000}=\frac{7}{12800}\) है। अंतिम उत्तर को हमेशा सरल रूप में लिखें।
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भिन्न \( \frac{61}{90} \) का दशमलव प्रसार कैसा होगा?
What type of decimal expansion will \( \frac{61}{90} \) have?
#number-systems
#decimal-representation
#recurring-test
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A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D मिश्रित पूर्णांक / Mixed integer
Explanation opens after your attempt
Correct Answer
B. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
\(90=2\times3^2\times5\) has (3), and the fraction is in simplest form. Therefore, the decimal will be non-terminating recurring.
Step 2
Why this answer is correct
The correct answer is B. असांत आवर्ती / Non-terminating recurring. \(90=2\times3^2\times5\) has (3), and the fraction is in simplest form. Therefore, the decimal will be non-terminating recurring.
Step 3
Exam Tip
\(90=2\times3^2\times5\) में (3) है और भिन्न सरल रूप में है। इसलिए दशमलव असांत आवर्ती होगा।
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दशमलव (7.500005) का विस्तारित रूप कौन-सा है?
Which is the expanded form of (7.500005)?
#number-systems
#decimal-representation
#expanded-form
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A \(7+\frac{5}{10}+\frac{5}{1000000}\)
B \(7+\frac{5}{100}+\frac{5}{100000}\)
C \(75+\frac{5}{1000000}\)
D \(7+\frac{500005}{1000}\)
Explanation opens after your attempt
Correct Answer
A. \(7+\frac{5}{10}+\frac{5}{1000000}\)
Step 1
Concept
The first (5) is in tenths and the last (5) is in millionths. Zero-value places need not be written separately.
Step 2
Why this answer is correct
The correct answer is A. \(7+\frac{5}{10}+\frac{5}{1000000}\). The first (5) is in tenths and the last (5) is in millionths. Zero-value places need not be written separately.
Step 3
Exam Tip
पहला (5) दसवें और अंतिम (5) दस लाखवें स्थान पर है। शून्य वाले स्थानों का मान अलग से लिखना आवश्यक नहीं है।
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\(0.864\div0.0018\) का मान क्या है?
What is the value of \(0.864\div0.0018\)?
#number-systems
#decimal-representation
#decimal-division
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A (48)
B (480)
C (4.8)
D (0.48)
Explanation opens after your attempt
Step 1
Concept
Multiplying both numbers by (10000) gives \(8640\div18=480\). Removing decimals makes division easier.
Step 2
Why this answer is correct
The correct answer is B. (480). Multiplying both numbers by (10000) gives \(8640\div18=480\). Removing decimals makes division easier.
Step 3
Exam Tip
दोनों संख्याओं को (10000) से गुणा करने पर \(8640\div18=480\) मिलता है। दशमलव हटाकर भाग देना आसान होता है।
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(15.009-8.34575) का मान क्या है?
What is the value of (15.009-8.34575)?
#number-systems
#decimal-representation
#decimal-subtraction
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A (6.66325)
B (6.67325)
C (7.33625)
D (6.56325)
Explanation opens after your attempt
Correct Answer
A. (6.66325)
Step 1
Concept
(15.009=15.00900), so (15.00900-8.34575=6.66325). Make decimal places equal while subtracting.
Step 2
Why this answer is correct
The correct answer is A. (6.66325). (15.009=15.00900), so (15.00900-8.34575=6.66325). Make decimal places equal while subtracting.
Step 3
Exam Tip
(15.009=15.00900), इसलिए (15.00900-8.34575=6.66325) है। घटाते समय दशमलव स्थान समान करें।
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(0.5625+0.001953125+0.0000390625) का मान क्या है?
What is the value of (0.5625+0.001953125+0.0000390625)?
#number-systems
#decimal-representation
#decimal-addition
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A (0.5644921875)
B (0.564453125)
C (0.5634921875)
D (0.5625390625)
Explanation opens after your attempt
Correct Answer
A. (0.5644921875)
Step 1
Concept
Writing equal decimal places gives (0.5625000000+0.0019531250+0.0000390625=0.5644921875). Align decimal points while adding.
Step 2
Why this answer is correct
The correct answer is A. (0.5644921875). Writing equal decimal places gives (0.5625000000+0.0019531250+0.0000390625=0.5644921875). Align decimal points while adding.
Step 3
Exam Tip
समान दशमलव स्थान लिखने पर (0.5625000000+0.0019531250+0.0000390625=0.5644921875) मिलता है। जोड़ में दशमलव बिंदु सीध में रखें।
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दशमलव \(19.874999\ldots\) किस सांत दशमलव के बराबर है?
The decimal \(19.874999\ldots\) is equal to which terminating decimal?
#number-systems
#decimal-representation
#recurring-decimal
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A (19.87)
B (19.875)
C (19.874)
D (19.9)
Explanation opens after your attempt
Correct Answer
B. (19.875)
Step 1
Concept
When (9)'s repeat continuously, the previous digit increases by (1). So \(19.874999\ldots=19.875\).
Step 2
Why this answer is correct
The correct answer is B. (19.875). When (9)'s repeat continuously, the previous digit increases by (1). So \(19.874999\ldots=19.875\).
Step 3
Exam Tip
लगातार (9) आने पर पिछला अंक (1) बढ़ जाता है। इसलिए \(19.874999\ldots=19.875\) है।
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कौन-सा दशमलव \( \frac{41}{80} \) से बड़ा और \( \frac{19}{37} \) से छोटा है?
Which decimal is greater than \( \frac{41}{80} \) and less than \( \frac{19}{37} \)?
#number-systems
#decimal-representation
#between-decimals
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A (0.5124)
B (0.5125)
C (0.5130)
D (0.5142)
Explanation opens after your attempt
Correct Answer
C. (0.5130)
Step 1
Concept
\( \frac{41}{80}=0.5125 \) and \( \frac{19}{37}=0.513513\ldots \), so (0.5130) lies between them. Convert the boundaries into decimals.
Step 2
Why this answer is correct
The correct answer is C. (0.5130). \( \frac{41}{80}=0.5125 \) and \( \frac{19}{37}=0.513513\ldots \), so (0.5130) lies between them. Convert the boundaries into decimals.
Step 3
Exam Tip
\( \frac{41}{80}=0.5125 \) और \( \frac{19}{37}=0.513513\ldots \), इसलिए (0.5130) इनके बीच है। सीमाओं को दशमलव में बदलें।
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यदि \(0.74a\leq0.745\), तो अंक (a) के कितने मान संभव हैं?
If \(0.74a\leq0.745\), how many values of digit (a) are possible?
#number-systems
#decimal-representation
#digit-comparison
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A (4)
B (6)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
At the thousandths place, \(a\leq5\) is needed. So (a=0,1,2,3,4,5), giving (6) possible values.
Step 2
Why this answer is correct
The correct answer is B. (6). At the thousandths place, \(a\leq5\) is needed. So (a=0,1,2,3,4,5), giving (6) possible values.
Step 3
Exam Tip
हजारवें स्थान पर \(a\leq5\) होना चाहिए। इसलिए (a=0,1,2,3,4,5), यानी (6) मान संभव हैं।
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दशमलव \(6.03003000300003\ldots\) किस संख्या-प्रकार को दर्शा सकता है?
The decimal \(6.03003000300003\ldots\) can represent which type of number?
#number-systems
#decimal-representation
#irrational-decimal
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A सांत परिमेय / Terminating rational
B असांत आवर्ती परिमेय / Non-terminating recurring rational
C अपरिमेय / Irrational
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
C. अपरिमेय / Irrational
Step 1
Concept
It is non-terminating and has no fixed repetition. Such a decimal can be the form of an irrational number.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय / Irrational. It is non-terminating and has no fixed repetition. Such a decimal can be the form of an irrational number.
Step 3
Exam Tip
यह असांत है और इसमें निश्चित दोहराव नहीं है। ऐसा दशमलव अपरिमेय संख्या का रूप हो सकता है।
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यदि (100000x=7.8125), तो (x) का मान क्या है?
If (100000x=7.8125), what is the value of (x)?
#number-systems
#decimal-representation
#decimal-division
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A (781250)
B (0.000078125)
C (0.0078125)
D (0.078125)
Explanation opens after your attempt
Correct Answer
B. (0.000078125)
Step 1
Concept
\(x=7.8125\div100000=0.000078125\). On dividing by (100000), the decimal moves five places left.
Step 2
Why this answer is correct
The correct answer is B. (0.000078125). \(x=7.8125\div100000=0.000078125\). On dividing by (100000), the decimal moves five places left.
Step 3
Exam Tip
\(x=7.8125\div100000=0.000078125\) है। (100000) से भाग देने पर दशमलव पांच स्थान बाईं ओर जाता है।
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दशमलव (43.009008) में (8) का स्थानीय मान क्या है?
What is the place value of (8) in (43.009008)?
#number-systems
#decimal-representation
#place-value
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A \( \frac{8}{1000} \)
B \( \frac{8}{10000} \)
C \( \frac{8}{100000} \)
D \( \frac{8}{1000000} \)
Explanation opens after your attempt
Correct Answer
D. \( \frac{8}{1000000} \)
Step 1
Concept
(8) is in the sixth place after the decimal point. So its place value is \( \frac{8}{1000000} \).
Step 2
Why this answer is correct
The correct answer is D. \( \frac{8}{1000000} \). (8) is in the sixth place after the decimal point. So its place value is \( \frac{8}{1000000} \).
Step 3
Exam Tip
(8) दशमलव के बाद छठे स्थान पर है। इसलिए उसका स्थानीय मान \( \frac{8}{1000000} \) है।
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(5.005), (5.0505), (5.0055), (5.500) का बढ़ता क्रम कौन-सा है?
What is the ascending order of (5.005), (5.0505), (5.0055), and (5.500)?
#number-systems
#decimal-representation
#ascending-order
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A (5.005<5.0055<5.0505<5.500)
B (5.0055<5.005<5.0505<5.500)
C (5.500<5.0505<5.0055<5.005)
D (5.005<5.0505<5.0055<5.500)
Explanation opens after your attempt
Correct Answer
A. (5.005<5.0055<5.0505<5.500)
Step 1
Concept
(5.005=5.0050), so (5.0055) is greater. Write equal decimal places for comparison.
Step 2
Why this answer is correct
The correct answer is A. (5.005<5.0055<5.0505<5.500). (5.005=5.0050), so (5.0055) is greater. Write equal decimal places for comparison.
Step 3
Exam Tip
(5.005=5.0050), इसलिए (5.0055) उससे बड़ा है। तुलना के लिए समान दशमलव स्थान लिखें।
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भिन्न \( \frac{181}{32000} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{181}{32000} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.00565625)
B (0.0565625)
C (0.018132)
D (0.000565625)
Explanation opens after your attempt
Correct Answer
A. (0.00565625)
Step 1
Concept
\(32000\times3125=100000000\), so \( \frac{181}{32000}=0.00565625 \). Convert the denominator into a power of (10) to get the exact decimal.
Step 2
Why this answer is correct
The correct answer is A. (0.00565625). \(32000\times3125=100000000\), so \( \frac{181}{32000}=0.00565625 \). Convert the denominator into a power of (10) to get the exact decimal.
Step 3
Exam Tip
\(32000\times3125=100000000\), इसलिए \( \frac{181}{32000}=0.00565625 \) है। हर को (10) की घात बनाकर सटीक दशमलव निकालें।
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दशमलव (0.000078125) की तुलना (0.0078125) से करने पर (0.0078125) कितने गुना है?
When (0.000078125) is compared with (0.0078125), how many times is (0.0078125)?
#number-systems
#decimal-representation
#decimal-comparison
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A (10) गुना / (10) times
B (100) गुना / (100) times
C (1000) गुना / (1000) times
D (1) गुना / (1) time
Explanation opens after your attempt
Correct Answer
B. (100) गुना / (100) times
Step 1
Concept
\(0.0078125\div0.000078125=100\). The difference in decimal places helps understand the ratio.
Step 2
Why this answer is correct
The correct answer is B. (100) गुना / (100) times. \(0.0078125\div0.000078125=100\). The difference in decimal places helps understand the ratio.
Step 3
Exam Tip
\(0.0078125\div0.000078125=100\) है। दशमलव स्थानों का अंतर अनुपात समझने में मदद करता है।
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यदि \(x=0.000\overline{54}\), तो इसका सामान्य दशमलव रूप क्या है?
If \(x=0.000\overline{54}\), what is its ordinary decimal form?
#number-systems
#decimal-representation
#bar-notation
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A \(0.000545454\ldots\)
B \(0.00005454\ldots\)
C \(0.00054054\ldots\)
D (0.00054)
Explanation opens after your attempt
Correct Answer
A. \(0.000545454\ldots\)
Step 1
Concept
After the first (000), (54) repeats again and again. So the decimal is \(0.000545454\ldots\).
Step 2
Why this answer is correct
The correct answer is A. \(0.000545454\ldots\). After the first (000), (54) repeats again and again. So the decimal is \(0.000545454\ldots\).
Step 3
Exam Tip
पहले (000) के बाद (54) बार-बार दोहरता है। इसलिए दशमलव \(0.000545454\ldots\) होगा।
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सरल रूप में \( \frac{625}{10000} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{625}{10000} \) have?
#number-systems
#decimal-representation
#simplest-form-test
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A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D केवल पूर्णांक / Integer only
Explanation opens after your attempt
Correct Answer
A. सांत / Terminating
Step 1
Concept
\( \frac{625}{10000}=\frac{1}{16} \) and \(16=2^4\). Therefore, the decimal will terminate.
Step 2
Why this answer is correct
The correct answer is A. सांत / Terminating. \( \frac{625}{10000}=\frac{1}{16} \) and \(16=2^4\). Therefore, the decimal will terminate.
Step 3
Exam Tip
\( \frac{625}{10000}=\frac{1}{16} \) और \(16=2^4\) है। इसलिए दशमलव सांत होगा।
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सरल रूप में \( \frac{132}{484} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{132}{484} \) have?
#number-systems
#decimal-representation
#simplest-form-test
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A सांत / Terminating
B असांत अनावर्ती / Non-terminating non-recurring
C असांत आवर्ती / Non-terminating recurring
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
C. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
\( \frac{132}{484}=\frac{3}{11} \), and the denominator has (11). So the decimal will be non-terminating recurring.
Step 2
Why this answer is correct
The correct answer is C. असांत आवर्ती / Non-terminating recurring. \( \frac{132}{484}=\frac{3}{11} \), and the denominator has (11). So the decimal will be non-terminating recurring.
Step 3
Exam Tip
\( \frac{132}{484}=\frac{3}{11} \) है और हर में (11) है। इसलिए दशमलव असांत आवर्ती होगा।
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दशमलव \(23.74999\ldots\) किस सांत दशमलव के बराबर है?
The decimal \(23.74999\ldots\) is equal to which terminating decimal?
#number-systems
#decimal-representation
#recurring-decimal
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A (23.74)
B (23.75)
C (23.749)
D (23.8)
Explanation opens after your attempt
Correct Answer
B. (23.75)
Step 1
Concept
When (9)'s repeat continuously, the previous digit increases by (1). So \(23.74999\ldots=23.75\).
Step 2
Why this answer is correct
The correct answer is B. (23.75). When (9)'s repeat continuously, the previous digit increases by (1). So \(23.74999\ldots=23.75\).
Step 3
Exam Tip
लगातार (9) आने पर पिछला अंक (1) बढ़ जाता है। इसलिए \(23.74999\ldots=23.75\) है।
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दशमलव (8.090600) में (6) का स्थानीय मान क्या है?
What is the place value of (6) in (8.090600)?
#number-systems
#decimal-representation
#place-value
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A \( \frac{6}{100} \)
B \( \frac{6}{1000} \)
C \( \frac{6}{10000} \)
D \( \frac{6}{100000} \)
Explanation opens after your attempt
Correct Answer
C. \( \frac{6}{10000} \)
Step 1
Concept
(6) is in the fourth place after the decimal point. The fourth decimal place is ten-thousandths.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{6}{10000} \). (6) is in the fourth place after the decimal point. The fourth decimal place is ten-thousandths.
Step 3
Exam Tip
(6) दशमलव के बाद चौथे स्थान पर है। चौथा दशमलव स्थान दस हजारवां होता है।
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यदि (a=0.708), (b=0.780), (c=0.7008), तो घटते क्रम में सही व्यवस्था कौन-सी है?
If (a=0.708), (b=0.780), (c=0.7008), which is the correct descending order?
#number-systems
#decimal-representation
#descending-order
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A (b>a>c)
B (a>b>c)
C (c>a>b)
D (b>c>a)
Explanation opens after your attempt
Correct Answer
A. (b>a>c)
Step 1
Concept
(0.780>0.708>0.7008). Compare all decimals after writing them up to equal places.
Step 2
Why this answer is correct
The correct answer is A. (b>a>c). (0.780>0.708>0.7008). Compare all decimals after writing them up to equal places.
Step 3
Exam Tip
(0.780>0.708>0.7008) है। सभी दशमलवों को समान स्थान तक लिखकर तुलना करें।
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कौन-सा विकल्प \( \frac{47}{500}+\frac{23}{1280} \) का दशमलव मान है?
Which option is the decimal value of \( \frac{47}{500}+\frac{23}{1280} \)?
#number-systems
#decimal-representation
#decimal-addition
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A (0.11196875)
B (0.12196875)
C (0.09496875)
D (0.10196875)
Explanation opens after your attempt
Correct Answer
A. (0.11196875)
Step 1
Concept
\( \frac{47}{500}=0.094 \) and \( \frac{23}{1280}=0.01796875 \), so the sum is (0.11196875). First convert the fractions into decimals.
Step 2
Why this answer is correct
The correct answer is A. (0.11196875). \( \frac{47}{500}=0.094 \) and \( \frac{23}{1280}=0.01796875 \), so the sum is (0.11196875). First convert the fractions into decimals.
Step 3
Exam Tip
\( \frac{47}{500}=0.094 \) और \( \frac{23}{1280}=0.01796875 \), इसलिए योग (0.11196875) है। पहले भिन्नों को दशमलव में बदलें।
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कौन-सा विकल्प \( \frac{59}{256}-0.10546875 \) का मान है?
Which option is the value of \( \frac{59}{256}-0.10546875 \)?
#number-systems
#decimal-representation
#decimal-subtraction
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A (0.125)
B (0.10546875)
C (0.23046875)
D (0.3359375)
Explanation opens after your attempt
Correct Answer
A. (0.125)
Step 1
Concept
\( \frac{59}{256}=0.23046875 \), so (0.23046875-0.10546875=0.125). Convert the fraction into decimal and subtract.
Step 2
Why this answer is correct
The correct answer is A. (0.125). \( \frac{59}{256}=0.23046875 \), so (0.23046875-0.10546875=0.125). Convert the fraction into decimal and subtract.
Step 3
Exam Tip
\( \frac{59}{256}=0.23046875 \), इसलिए (0.23046875-0.10546875=0.125) है। भिन्न को दशमलव में बदलकर घटाएं।
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(1.134) को (0.018) से भाग देने पर क्या मिलेगा?
What is obtained by dividing (1.134) by (0.018)?
#number-systems
#decimal-representation
#decimal-division
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A (6.3)
B (63)
C (630)
D (0.63)
Explanation opens after your attempt
Step 1
Concept
Multiplying both by (1000) gives \(1134\div18=63\). Removing decimals makes division easier.
Step 2
Why this answer is correct
The correct answer is B. (63). Multiplying both by (1000) gives \(1134\div18=63\). Removing decimals makes division easier.
Step 3
Exam Tip
दोनों को (1000) से गुणा करने पर \(1134\div18=63\) मिलता है। दशमलव हटाकर भाग देना आसान होता है।
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दशमलव \(0.0747474\ldots\) को बार संकेतन में कैसे लिखेंगे?
How is \(0.0747474\ldots\) written in bar notation?
#number-systems
#decimal-representation
#bar-notation
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A \(0.\overline{074}\)
B \(0.0\overline{74}\)
C \(0.07\overline{4}\)
D \(0.\overline{74}\)
Explanation opens after your attempt
Correct Answer
B. \(0.0\overline{74}\)
Step 1
Concept
After the first (0), (74) repeats continuously. The bar will be placed only over (74).
Step 2
Why this answer is correct
The correct answer is B. \(0.0\overline{74}\). After the first (0), (74) repeats continuously. The bar will be placed only over (74).
Step 3
Exam Tip
पहले (0) के बाद (74) लगातार दोहरता है। बार केवल (74) पर लगाया जाएगा।
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भिन्न \( \frac{47}{88} \) का दशमलव प्रसार कौन-सा है?
Which is the decimal expansion of \( \frac{47}{88} \)?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.534090909\ldots\)
B \(0.474747\ldots\)
C \(0.538888\ldots\)
D \(0.88047\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(0.534090909\ldots\)
Step 1
Concept
\(47\div88=0.534090909\ldots\). In long division, the block (09) repeats.
Step 2
Why this answer is correct
The correct answer is A. \(0.534090909\ldots\). \(47\div88=0.534090909\ldots\). In long division, the block (09) repeats.
Step 3
Exam Tip
\(47\div88=0.534090909\ldots\) होता है। लंबी भाग विधि में (09) का समूह दोहरता है।
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यदि \( \frac{p}{q} \) सरल रूप में है और \(q=2^{11}\), तो सांत दशमलव में अधिकतम कितने दशमलव स्थान होंगे?
If \( \frac{p}{q} \) is in simplest form and \(q=2^{11}\), what is the maximum number of decimal places in the terminating decimal?
#number-systems
#decimal-representation
#decimal-places
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
To make \(2^{11}\) into \(10^{11}\), we multiply by \(5^{11}\). So there will be at most (11) decimal places.
Step 2
Why this answer is correct
The correct answer is C. (11). To make \(2^{11}\) into \(10^{11}\), we multiply by \(5^{11}\). So there will be at most (11) decimal places.
Step 3
Exam Tip
\(2^{11}\) को \(10^{11}\) बनाने के लिए \(5^{11}\) से गुणा करना पड़ेगा। इसलिए अधिकतम (11) दशमलव स्थान होंगे।
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यदि \( \frac{p}{q} \) सरल रूप में है और \(q=2^6\times5^9\), तो सांत दशमलव में अधिकतम कितने दशमलव स्थान होंगे?
If \( \frac{p}{q} \) is in simplest form and \(q=2^6\times5^9\), what is the maximum number of decimal places in the terminating decimal?
#number-systems
#decimal-representation
#decimal-places
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A (6)
B (9)
C (15)
D (54)
Explanation opens after your attempt
Step 1
Concept
The larger exponent among (2) and (5) is (9). So the terminating decimal will have at most (9) places.
Step 2
Why this answer is correct
The correct answer is B. (9). The larger exponent among (2) and (5) is (9). So the terminating decimal will have at most (9) places.
Step 3
Exam Tip
(2) और (5) की घातों में बड़ी घात (9) है। इसलिए सांत दशमलव में अधिकतम (9) स्थान होंगे।
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दशमलव \(0.06006000600006\ldots\) किस प्रकार का है?
What type of decimal is \(0.06006000600006\ldots\)?
#number-systems
#decimal-representation
#non-recurring-decimal
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A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D सांत परिमेय / Terminating rational
Explanation opens after your attempt
Correct Answer
C. असांत अनावर्ती / Non-terminating non-recurring
Step 1
Concept
The number of zeros between (6)'s increases, so there is no fixed repetition. Such a decimal is non-terminating non-recurring.
Step 2
Why this answer is correct
The correct answer is C. असांत अनावर्ती / Non-terminating non-recurring. The number of zeros between (6)'s increases, so there is no fixed repetition. Such a decimal is non-terminating non-recurring.
Step 3
Exam Tip
इसमें (6) के बीच शून्यों की संख्या बढ़ती है, इसलिए कोई निश्चित दोहराव नहीं है। ऐसा दशमलव असांत अनावर्ती होता है।
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(0.0064) को प्रतिशत में बदलने पर क्या मिलेगा?
What is obtained by converting (0.0064) into a percentage?
#number-systems
#decimal-representation
#decimal-percent
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A (0.064%)
B (0.64%)
C (6.4%)
D (64%)
Explanation opens after your attempt
Correct Answer
B. (0.64%)
Step 1
Concept
\(0.0064\times100=0.64\), so it is (0.64%). Multiply by (100) to convert into percentage.
Step 2
Why this answer is correct
The correct answer is B. (0.64%). \(0.0064\times100=0.64\), so it is (0.64%). Multiply by (100) to convert into percentage.
Step 3
Exam Tip
\(0.0064\times100=0.64\), इसलिए (0.64%) है। प्रतिशत में बदलने के लिए (100) से गुणा करें।
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(0.00048828125) को (10000000) से गुणा करने पर क्या मिलेगा?
What is obtained by multiplying (0.00048828125) by (10000000)?
#number-systems
#decimal-representation
#decimal-multiplication
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A (48.828125)
B (488.28125)
C (4882.8125)
D (48828.125)
Explanation opens after your attempt
Correct Answer
C. (4882.8125)
Step 1
Concept
On multiplying by (10000000), the decimal point moves seven places to the right. Therefore, the answer is (4882.8125).
Step 2
Why this answer is correct
The correct answer is C. (4882.8125). On multiplying by (10000000), the decimal point moves seven places to the right. Therefore, the answer is (4882.8125).
Step 3
Exam Tip
(10000000) से गुणा करने पर दशमलव बिंदु सात स्थान दाईं ओर जाता है। इसलिए उत्तर (4882.8125) है।
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\(0.374\overline{9}\), (0.375), \( \frac{3}{8} \) के बारे में सही कथन कौन-सा है?
Which statement about \(0.374\overline{9}\), (0.375), and \( \frac{3}{8} \) is correct?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.374\overline{9}<0.375=\frac{3}{8}\)
B \(0.375<0.374\overline{9}<\frac{3}{8}\)
C \(0.374\overline{9}=0.375=\frac{3}{8}\)
D \( \frac{3}{8}<0.374\overline{9}<0.375 \)
Explanation opens after your attempt
Correct Answer
C. \(0.374\overline{9}=0.375=\frac{3}{8}\)
Step 1
Concept
\(0.374\overline{9}=0.375000\ldots\) and \( \frac{3}{8}=0.375 \). Identify repeating (9)'s correctly.
Step 2
Why this answer is correct
The correct answer is C. \(0.374\overline{9}=0.375=\frac{3}{8}\). \(0.374\overline{9}=0.375000\ldots\) and \( \frac{3}{8}=0.375 \). Identify repeating (9)'s correctly.
Step 3
Exam Tip
\(0.374\overline{9}=0.375000\ldots\) और \( \frac{3}{8}=0.375 \) है। दोहरते (9) को सही पहचानें।
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कौन-सा दशमलव \( \frac{47}{128} \) से बड़ा और (0.368) से छोटा है?
Which decimal is greater than \( \frac{47}{128} \) and less than (0.368)?
#number-systems
#decimal-representation
#between-decimals
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A (0.3670)
B (0.3675)
C (0.3680)
D (0.3690)
Explanation opens after your attempt
Correct Answer
B. (0.3675)
Step 1
Concept
\( \frac{47}{128}=0.3671875 \), so (0.3675) is greater than (0.3671875) and less than (0.368). Convert boundary values into decimals.
Step 2
Why this answer is correct
The correct answer is B. (0.3675). \( \frac{47}{128}=0.3671875 \), so (0.3675) is greater than (0.3671875) and less than (0.368). Convert boundary values into decimals.
Step 3
Exam Tip
\( \frac{47}{128}=0.3671875 \), इसलिए (0.3675), (0.3671875) से बड़ा और (0.368) से छोटा है। सीमा मानों को दशमलव में बदलें।
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सरल रूप में \( \frac{242}{605} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{242}{605} \) have?
#number-systems
#decimal-representation
#simplest-form-test
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A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
A. सांत / Terminating
Step 1
Concept
\( \frac{242}{605}=\frac{2}{5} \), and the denominator has only (5). Therefore, the decimal will terminate.
Step 2
Why this answer is correct
The correct answer is A. सांत / Terminating. \( \frac{242}{605}=\frac{2}{5} \), and the denominator has only (5). Therefore, the decimal will terminate.
Step 3
Exam Tip
\( \frac{242}{605}=\frac{2}{5} \) और हर में केवल (5) है। इसलिए दशमलव सांत होगा।
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भिन्न \( \frac{313}{128000} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{313}{128000} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.024453125)
B (0.0024453125)
C (0.00024453125)
D (0.313128)
Explanation opens after your attempt
Correct Answer
B. (0.0024453125)
Step 1
Concept
\( \frac{313}{128000}=0.0024453125 \). Convert the denominator into a power of (10) to get the exact decimal.
Step 2
Why this answer is correct
The correct answer is B. (0.0024453125). \( \frac{313}{128000}=0.0024453125 \). Convert the denominator into a power of (10) to get the exact decimal.
Step 3
Exam Tip
\( \frac{313}{128000}=0.0024453125 \) है। हर को (10) की घात में बदलकर सटीक दशमलव निकालें।
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दशमलव (0.00003125) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.00003125) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{1}{3200} \)
B \( \frac{1}{3125} \)
C \( \frac{1}{32000} \)
D \( \frac{3125}{1000000} \)
Explanation opens after your attempt
Correct Answer
C. \( \frac{1}{32000} \)
Step 1
Concept
\(0.00003125=\frac{3125}{100000000}=\frac{1}{32000}\). Count decimal places and simplify the fraction.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{1}{32000} \). \(0.00003125=\frac{3125}{100000000}=\frac{1}{32000}\). Count decimal places and simplify the fraction.
Step 3
Exam Tip
\(0.00003125=\frac{3125}{100000000}=\frac{1}{32000}\) है। दशमलव स्थान गिनकर भिन्न को सरल करें।
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यदि \( \frac{p}{q} \) सरल रूप में है और \(q=2^7\times5^4\times29\), तो दशमलव प्रसार कैसा होगा?
If \( \frac{p}{q} \) is in simplest form and \(q=2^7\times5^4\times29\), what type of decimal expansion will it have?
#number-systems
#decimal-representation
#prime-factor-test
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A असांत आवर्ती / Non-terminating recurring
B सांत / Terminating
C असांत अनावर्ती / Non-terminating non-recurring
D केवल पूर्णांक / Integer only
Explanation opens after your attempt
Correct Answer
A. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
The denominator has (29), a factor other than (2) and (5). So the rational number will have a non-terminating recurring decimal.
Step 2
Why this answer is correct
The correct answer is A. असांत आवर्ती / Non-terminating recurring. The denominator has (29), a factor other than (2) and (5). So the rational number will have a non-terminating recurring decimal.
Step 3
Exam Tip
हर में (29) है, जो (2) और (5) के अलावा गुणनखंड है। इसलिए परिमेय संख्या का दशमलव असांत आवर्ती होगा।
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दशमलव \(0.000919191\ldots\) का सही बार संकेतन कौन-सा है?
Which is the correct bar notation of \(0.000919191\ldots\)?
#number-systems
#decimal-representation
#bar-notation
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A \(0.\overline{00091}\)
B \(0.000\overline{91}\)
C \(0.0009\overline{1}\)
D \(0.00\overline{091}\)
Explanation opens after your attempt
Correct Answer
B. \(0.000\overline{91}\)
Step 1
Concept
After the first (000), the block (91) repeats. Put the bar only over the actual recurring part.
Step 2
Why this answer is correct
The correct answer is B. \(0.000\overline{91}\). After the first (000), the block (91) repeats. Put the bar only over the actual recurring part.
Step 3
Exam Tip
पहले (000) के बाद (91) का समूह दोहरता है। बार केवल वास्तविक आवर्ती भाग पर लगाएं।
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यदि \(0.58a4\geq0.5864\), तो अंक (a) के कितने मान संभव हैं?
If \(0.58a4\geq0.5864\), how many values of digit (a) are possible?
#number-systems
#decimal-representation
#digit-comparison
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
At the thousandths place, \(a\geq6\) is needed. So (a=6,7,8,9), giving (4) possible values.
Step 2
Why this answer is correct
The correct answer is C. (4). At the thousandths place, \(a\geq6\) is needed. So (a=6,7,8,9), giving (4) possible values.
Step 3
Exam Tip
हजारवें स्थान पर \(a\geq6\) होना चाहिए। इसलिए (a=6,7,8,9), यानी (4) मान संभव हैं।
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यदि \( \frac{p}{q} \) सरल रूप में है और \(q=2^9\times5^{12}\), तो सांत दशमलव में अधिकतम कितने दशमलव स्थान होंगे?
If \( \frac{p}{q} \) is in simplest form and \(q=2^9\times5^{12}\), what is the maximum number of decimal places in the terminating decimal?
#number-systems
#decimal-representation
#decimal-places
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
The larger exponent among (2) and (5) is (12). So the terminating decimal will have at most (12) places.
Step 2
Why this answer is correct
The correct answer is D. (12). The larger exponent among (2) and (5) is (12). So the terminating decimal will have at most (12) places.
Step 3
Exam Tip
(2) और (5) की घातों में बड़ी घात (12) है। इसलिए सांत दशमलव में अधिकतम (12) स्थान होंगे।
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