भिन्न \( \frac{7}{40} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{7}{40} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.175)
B (0.075)
C (0.740)
D (1.75)
Explanation opens after your attempt
Correct Answer
A. (0.175)
Step 1
Concept
\( \frac{7}{40}=\frac{175}{1000}=0.175 \). Making the denominator (1000) gives the decimal quickly.
Step 2
Why this answer is correct
The correct answer is A. (0.175). \( \frac{7}{40}=\frac{175}{1000}=0.175 \). Making the denominator (1000) gives the decimal quickly.
Step 3
Exam Tip
\( \frac{7}{40}=\frac{175}{1000}=0.175 \) है। हर को (1000) बनाने से दशमलव जल्दी मिलता है।
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भिन्न \( \frac{19}{80} \) का दशमलव रूप कौन-सा है?
Which is the decimal form of \( \frac{19}{80} \)?
#number-systems
#decimal-representation
#terminating-decimal
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A (0.198)
B (0.2375)
C (0.238)
D (0.80)
Explanation opens after your attempt
Correct Answer
B. (0.2375)
Step 1
Concept
\(80\times125=10000\), so \( \frac{19}{80}=\frac{2375}{10000}=0.2375 \). Make the denominator a power of (10).
Step 2
Why this answer is correct
The correct answer is B. (0.2375). \(80\times125=10000\), so \( \frac{19}{80}=\frac{2375}{10000}=0.2375 \). Make the denominator a power of (10).
Step 3
Exam Tip
\(80\times125=10000\), इसलिए \( \frac{19}{80}=\frac{2375}{10000}=0.2375 \) है। हर को (10) की घात बनाएं।
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दशमलव (0.3125) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.3125) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{31}{100} \)
B \( \frac{3125}{1000} \)
C \( \frac{5}{16} \)
D \( \frac{25}{80} \)
Explanation opens after your attempt
Correct Answer
C. \( \frac{5}{16} \)
Step 1
Concept
\(0.3125=\frac{3125}{10000}=\frac{5}{16}\). Convert the decimal to a fraction and simplify it.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{5}{16} \). \(0.3125=\frac{3125}{10000}=\frac{5}{16}\). Convert the decimal to a fraction and simplify it.
Step 3
Exam Tip
\(0.3125=\frac{3125}{10000}=\frac{5}{16}\) है। दशमलव को भिन्न में बदलकर सरल करें।
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सरल रूप में \( \frac{13}{150} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{13}{150} \) have?
#number-systems
#decimal-representation
#decimal-type
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A सांत / Terminating
B असांत अनावर्ती / Non-terminating non-recurring
C पूर्णांक / Integer
D असांत आवर्ती / Non-terminating recurring
Explanation opens after your attempt
Correct Answer
D. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
\(150=2\times3\times5^2\) also has (3). Since it is rational, it will give a non-terminating recurring decimal.
Step 2
Why this answer is correct
The correct answer is D. असांत आवर्ती / Non-terminating recurring. \(150=2\times3\times5^2\) also has (3). Since it is rational, it will give a non-terminating recurring decimal.
Step 3
Exam Tip
\(150=2\times3\times5^2\) में (3) भी है। परिमेय संख्या होने से यह असांत आवर्ती दशमलव देगी।
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दशमलव (2.045) का विस्तारित रूप कौन-सा है?
Which is the expanded form of (2.045)?
#number-systems
#decimal-representation
#expanded-form
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A \(2+\frac{4}{100}+\frac{5}{1000}\)
B \(2+\frac{4}{10}+\frac{5}{100}\)
C \(2+\frac{45}{100}\)
D \(20+\frac{45}{1000}\)
Explanation opens after your attempt
Correct Answer
A. \(2+\frac{4}{100}+\frac{5}{1000}\)
Step 1
Concept
(4) is in the hundredths place and (5) is in the thousandths place. So \(2.045=2+\frac{4}{100}+\frac{5}{1000}\).
Step 2
Why this answer is correct
The correct answer is A. \(2+\frac{4}{100}+\frac{5}{1000}\). (4) is in the hundredths place and (5) is in the thousandths place. So \(2.045=2+\frac{4}{100}+\frac{5}{1000}\).
Step 3
Exam Tip
(4) सौवें और (5) हजारवें स्थान पर है। इसलिए \(2.045=2+\frac{4}{100}+\frac{5}{1000}\) है।
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कौन-सा दशमलव \( \frac{5}{12} \) के बराबर है?
Which decimal is equal to \( \frac{5}{12} \)?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.41666\ldots\)
B \(0.51212\ldots\)
C (0.45)
D (0.512)
Explanation opens after your attempt
Correct Answer
A. \(0.41666\ldots\)
Step 1
Concept
\(5\div12=0.41666\ldots\). While dividing, identify the repeating remainder.
Step 2
Why this answer is correct
The correct answer is A. \(0.41666\ldots\). \(5\div12=0.41666\ldots\). While dividing, identify the repeating remainder.
Step 3
Exam Tip
\(5\div12=0.41666\ldots\) होता है। भाग देते समय दोहराने वाले शेष को पहचानें।
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कौन-सी संख्या (0.56) और (0.57) के बीच आती है?
Which number lies between (0.56) and (0.57)?
#number-systems
#decimal-representation
#between-decimals
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A (0.559)
B (0.570)
C (0.565)
D (0.575)
Explanation opens after your attempt
Correct Answer
C. (0.565)
Step 1
Concept
(0.565) is greater than (0.560) and less than (0.570). Make decimal places equal while comparing.
Step 2
Why this answer is correct
The correct answer is C. (0.565). (0.565) is greater than (0.560) and less than (0.570). Make decimal places equal while comparing.
Step 3
Exam Tip
(0.565), (0.560) से बड़ा और (0.570) से छोटा है। तुलना में दशमलव स्थान समान करें।
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सरल रूप में \( \frac{21}{125} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{21}{125} \) have?
#number-systems
#decimal-representation
#terminating-test
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A असांत आवर्ती / Non-terminating recurring
B असांत अनावर्ती / Non-terminating non-recurring
C सांत / Terminating
D केवल पूर्णांक / Integer only
Explanation opens after your attempt
Correct Answer
C. सांत / Terminating
Step 1
Concept
\(125=5^3\), so the denominator has only (5). A fraction with such a denominator gives a terminating decimal.
Step 2
Why this answer is correct
The correct answer is C. सांत / Terminating. \(125=5^3\), so the denominator has only (5). A fraction with such a denominator gives a terminating decimal.
Step 3
Exam Tip
\(125=5^3\) है, इसलिए हर में केवल (5) है। ऐसे हर वाली भिन्न सांत दशमलव देती है।
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दशमलव (3.125) को अनुचित भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (3.125) is converted into an improper fraction?
#number-systems
#decimal-representation
#improper-fraction
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A \( \frac{25}{8} \)
B \( \frac{31}{25} \)
C \( \frac{125}{40} \)
D \( \frac{3}{125} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{25}{8} \)
Step 1
Concept
\(3.125=\frac{3125}{1000}=\frac{25}{8}\). Write the final answer in simplest form.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{25}{8} \). \(3.125=\frac{3125}{1000}=\frac{25}{8}\). Write the final answer in simplest form.
Step 3
Exam Tip
\(3.125=\frac{3125}{1000}=\frac{25}{8}\) है। अंतिम उत्तर को सरल रूप में लिखें।
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दशमलव \(0.0808\ldots\) का सही बार संकेतन कौन-सा है?
Which is the correct bar notation of \(0.0808\ldots\)?
#number-systems
#decimal-representation
#bar-notation
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A \(0.\overline{8}\)
B \(0.0\overline{8}\)
C \(0.\overline{08}\)
D (0.08)
Explanation opens after your attempt
Correct Answer
C. \(0.\overline{08}\)
Step 1
Concept
The block (08) repeats continuously. The bar is placed over the whole repeating block (08).
Step 2
Why this answer is correct
The correct answer is C. \(0.\overline{08}\). The block (08) repeats continuously. The bar is placed over the whole repeating block (08).
Step 3
Exam Tip
(08) का समूह लगातार दोहर रहा है। बार पूरे दोहराने वाले समूह (08) पर लगेगा।
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भिन्न \( \frac{29}{250} \) का दशमलव रूप क्या होगा?
What will be the decimal form of \( \frac{29}{250} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.116)
B (0.29)
C (0.250)
D (1.16)
Explanation opens after your attempt
Correct Answer
A. (0.116)
Step 1
Concept
\( \frac{29}{250}=\frac{116}{1000}=0.116 \). Multiply denominator (250) by (4) to make (1000).
Step 2
Why this answer is correct
The correct answer is A. (0.116). \( \frac{29}{250}=\frac{116}{1000}=0.116 \). Multiply denominator (250) by (4) to make (1000).
Step 3
Exam Tip
\( \frac{29}{250}=\frac{116}{1000}=0.116 \) है। हर (250) को (1000) बनाने के लिए (4) से गुणा करें।
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दशमलव (4.006) में (6) का स्थानीय मान क्या है?
What is the place value of (6) in (4.006)?
#number-systems
#decimal-representation
#place-value
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A \( \frac{6}{10} \)
B \( \frac{6}{100} \)
C \( \frac{6}{1000} \)
D (6)
Explanation opens after your attempt
Correct Answer
C. \( \frac{6}{1000} \)
Step 1
Concept
(6) is in the third place after the decimal point. The third decimal place is thousandths.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{6}{1000} \). (6) is in the third place after the decimal point. The third decimal place is thousandths.
Step 3
Exam Tip
(6) दशमलव के बाद तीसरे स्थान पर है। तीसरा दशमलव स्थान हजारवां होता है।
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दशमलव (0.00064) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.00064) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{64}{1000} \)
B \( \frac{8}{12500} \)
C \( \frac{4}{6250} \)
D \( \frac{16}{2500} \)
Explanation opens after your attempt
Correct Answer
B. \( \frac{8}{12500} \)
Step 1
Concept
\(0.00064=\frac{64}{100000}=\frac{8}{12500}\). For five decimal places, use denominator (100000).
Step 2
Why this answer is correct
The correct answer is B. \( \frac{8}{12500} \). \(0.00064=\frac{64}{100000}=\frac{8}{12500}\). For five decimal places, use denominator (100000).
Step 3
Exam Tip
\(0.00064=\frac{64}{100000}=\frac{8}{12500}\) है। पांच दशमलव स्थान हों तो हर (100000) लें।
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यदि (x=0.37) और (y=0.307), तो कौन-सा संबंध सही है?
If (x=0.37) and (y=0.307), which relation is correct?
#number-systems
#decimal-representation
#compare-decimals
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A (x<y)
B (x=y)
C (x>y)
D (x=0)
Explanation opens after your attempt
Step 1
Concept
(0.37=0.370), which is greater than (0.307). Write equal decimal places for comparison.
Step 2
Why this answer is correct
The correct answer is C. (x>y). (0.37=0.370), which is greater than (0.307). Write equal decimal places for comparison.
Step 3
Exam Tip
(0.37=0.370), जो (0.307) से बड़ा है। तुलना में दशमलव स्थान समान लिखें।
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भिन्न \( \frac{1}{6} \) का दशमलव प्रसार कौन-सा है?
Which is the decimal expansion of \( \frac{1}{6} \)?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.1666\ldots\)
B (0.16)
C \(0.6161\ldots\)
D (0.6)
Explanation opens after your attempt
Correct Answer
A. \(0.1666\ldots\)
Step 1
Concept
\(1\div6=0.1666\ldots\). Here (6) is the repeating digit.
Step 2
Why this answer is correct
The correct answer is A. \(0.1666\ldots\). \(1\div6=0.1666\ldots\). Here (6) is the repeating digit.
Step 3
Exam Tip
\(1\div6=0.1666\ldots\) होता है। यहां (6) दोहराने वाला अंक है।
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दशमलव \(6.312312312\ldots\) में आवर्ती भाग कौन-सा है?
What is the recurring part in \(6.312312312\ldots\)?
#number-systems
#decimal-representation
#repeating-block
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A (31)
B (12)
C (312)
D (231)
Explanation opens after your attempt
Step 1
Concept
The block (312) repeats continuously. The recurring part is the smallest repeating block.
Step 2
Why this answer is correct
The correct answer is C. (312). The block (312) repeats continuously. The recurring part is the smallest repeating block.
Step 3
Exam Tip
(312) का समूह लगातार दोहर रहा है। आवर्ती भाग सबसे छोटा दोहराने वाला समूह होता है।
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दशमलव (0.4375) किस सरल भिन्न के बराबर है?
The decimal (0.4375) is equal to which simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{7}{16} \)
B \( \frac{35}{80} \)
C \( \frac{4375}{1000} \)
D \( \frac{4}{375} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{7}{16} \)
Step 1
Concept
\(0.4375=\frac{4375}{10000}=\frac{7}{16}\). First write the decimal with denominator (10000).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{7}{16} \). \(0.4375=\frac{4375}{10000}=\frac{7}{16}\). First write the decimal with denominator (10000).
Step 3
Exam Tip
\(0.4375=\frac{4375}{10000}=\frac{7}{16}\) है। दशमलव को पहले (10000) के हर में लिखें।
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(0.025) को प्रतिशत में बदलने पर क्या मिलेगा?
What is obtained by converting (0.025) into a percentage?
#number-systems
#decimal-representation
#decimal-percent
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A (25%)
B (0.25%)
C (2.5%)
D (0.025%)
Explanation opens after your attempt
Step 1
Concept
\(0.025\times100=2.5\), so it gives (2.5%). To convert a decimal into a percentage, multiply by (100).
Step 2
Why this answer is correct
The correct answer is C. (2.5%). \(0.025\times100=2.5\), so it gives (2.5%). To convert a decimal into a percentage, multiply by (100).
Step 3
Exam Tip
\(0.025\times100=2.5\), इसलिए (2.5%) मिलता है। दशमलव को प्रतिशत में बदलने के लिए (100) से गुणा करें।
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(5.08) को (100) से गुणा करने पर क्या मिलेगा?
What is obtained by multiplying (5.08) by (100)?
#number-systems
#decimal-representation
#decimal-multiplication
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A (0.508)
B (50.8)
C (508)
D (5080)
Explanation opens after your attempt
Step 1
Concept
\(5.08\times100=508\). On multiplying by (100), the decimal point moves two places to the right.
Step 2
Why this answer is correct
The correct answer is C. (508). \(5.08\times100=508\). On multiplying by (100), the decimal point moves two places to the right.
Step 3
Exam Tip
\(5.08\times100=508\) होता है। (100) से गुणा करने पर दशमलव बिंदु दो स्थान दाईं ओर जाता है।
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(37.5) को (1000) से भाग देने पर क्या मिलेगा?
What is obtained by dividing (37.5) by (1000)?
#number-systems
#decimal-representation
#decimal-division
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A (0.0375)
B (0.375)
C (3.75)
D (37500)
Explanation opens after your attempt
Correct Answer
A. (0.0375)
Step 1
Concept
\(37.5\div1000=0.0375\). On dividing by (1000), the decimal point moves three places to the left.
Step 2
Why this answer is correct
The correct answer is A. (0.0375). \(37.5\div1000=0.0375\). On dividing by (1000), the decimal point moves three places to the left.
Step 3
Exam Tip
\(37.5\div1000=0.0375\) है। (1000) से भाग देने पर दशमलव बिंदु तीन स्थान बाईं ओर जाता है।
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(0.48+0.075) का मान क्या है?
What is the value of (0.48+0.075)?
#number-systems
#decimal-representation
#decimal-addition
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A (0.123)
B (0.555)
C (0.5075)
D (0.795)
Explanation opens after your attempt
Correct Answer
B. (0.555)
Step 1
Concept
(0.48=0.480), so (0.480+0.075=0.555). Align decimal points while adding.
Step 2
Why this answer is correct
The correct answer is B. (0.555). (0.48=0.480), so (0.480+0.075=0.555). Align decimal points while adding.
Step 3
Exam Tip
(0.48=0.480), इसलिए (0.480+0.075=0.555) है। जोड़ते समय दशमलव बिंदु एक सीध में रखें।
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(3.2-0.875) का मान क्या है?
What is the value of (3.2-0.875)?
#number-systems
#decimal-representation
#decimal-subtraction
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A (2.325)
B (2.425)
C (3.075)
D (2.875)
Explanation opens after your attempt
Correct Answer
A. (2.325)
Step 1
Concept
(3.2=3.200), so (3.200-0.875=2.325). Add zeros in empty places while subtracting.
Step 2
Why this answer is correct
The correct answer is A. (2.325). (3.2=3.200), so (3.200-0.875=2.325). Add zeros in empty places while subtracting.
Step 3
Exam Tip
(3.2=3.200), इसलिए (3.200-0.875=2.325) है। घटाते समय खाली स्थानों में शून्य लगाएं।
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दशमलव (9.090) किसके बराबर है?
The decimal (9.090) is equal to which of the following?
#number-systems
#decimal-representation
#equivalent-decimals
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A (9.9)
B (9.009)
C (9.09)
D (90.90)
Explanation opens after your attempt
Step 1
Concept
A zero at the end of a decimal does not change its value. Therefore, (9.090=9.09).
Step 2
Why this answer is correct
The correct answer is C. (9.09). A zero at the end of a decimal does not change its value. Therefore, (9.090=9.09).
Step 3
Exam Tip
दशमलव के अंत का शून्य मान नहीं बदलता। इसलिए (9.090=9.09) है।
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(0.125), (0.152), (0.1205), (0.15) में सबसे बड़ी संख्या कौन-सी है?
Among (0.125), (0.152), (0.1205), and (0.15), which number is the greatest?
#number-systems
#decimal-representation
#compare-decimals
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A (0.125)
B (0.152)
C (0.1205)
D (0.15)
Explanation opens after your attempt
Correct Answer
B. (0.152)
Step 1
Concept
(0.1520) is greater than (0.1500), (0.1250), and (0.1205). Write all numbers up to equal decimal places for comparison.
Step 2
Why this answer is correct
The correct answer is B. (0.152). (0.1520) is greater than (0.1500), (0.1250), and (0.1205). Write all numbers up to equal decimal places for comparison.
Step 3
Exam Tip
(0.1520), (0.1500), (0.1250) और (0.1205) से बड़ा है। तुलना में सभी को समान दशमलव स्थान तक लिखें।
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दशमलव \(1.2303030\ldots\) में आवर्ती भाग कौन-सा है?
What is the recurring part in \(1.2303030\ldots\)?
#number-systems
#decimal-representation
#repeating-block
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A (23)
B (30)
C (03)
D (230)
Explanation opens after your attempt
Step 1
Concept
After (12) in the decimal part, (03) repeats. The recurring part is the part that repeats continuously.
Step 2
Why this answer is correct
The correct answer is C. (03). After (12) in the decimal part, (03) repeats. The recurring part is the part that repeats continuously.
Step 3
Exam Tip
दशमलव में (12) के बाद (03) बार-बार आ रहा है। आवर्ती भाग वही है जो लगातार दोहरता है।
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भिन्न \( \frac{4}{11} \) का दशमलव प्रसार कौन-सा है?
Which is the decimal expansion of \( \frac{4}{11} \)?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.363636\ldots\)
B \(0.444\ldots\)
C \(0.41111\ldots\)
D \(0.0404\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(0.363636\ldots\)
Step 1
Concept
\(4\div11=0.363636\ldots\). Here the block (36) repeats.
Step 2
Why this answer is correct
The correct answer is A. \(0.363636\ldots\). \(4\div11=0.363636\ldots\). Here the block (36) repeats.
Step 3
Exam Tip
\(4\div11=0.363636\ldots\) होता है। यहां (36) का समूह दोहरता है।
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किस विकल्प में सभी संख्याएं सांत दशमलव हैं?
In which option are all numbers terminating decimals?
#number-systems
#decimal-representation
#terminating-decimal
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A (0.25), (1.125), (3.04)
B \(0.\overline{3}\), (2.5), (4.6)
C \(1.2323\ldots\), (0.75), (9.1)
D \(0.101001\ldots\), (6.2), (8.0)
Explanation opens after your attempt
Correct Answer
A. (0.25), (1.125), (3.04)
Step 1
Concept
All numbers in the first option end after a finite number of digits. A terminating decimal has finite digits.
Step 2
Why this answer is correct
The correct answer is A. (0.25), (1.125), (3.04). All numbers in the first option end after a finite number of digits. A terminating decimal has finite digits.
Step 3
Exam Tip
पहले विकल्प की सभी संख्याएं कुछ अंकों के बाद समाप्त हो जाती हैं। सांत दशमलव में अंकों की संख्या सीमित होती है।
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किस विकल्प में दी गई संख्या अपरिमेय हो सकती है?
Which option can represent an irrational number?
#number-systems
#decimal-representation
#irrational-decimal
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A (0.625)
B \(0.\overline{54}\)
C \(2.01001000100001\ldots\) बिना निश्चित दोहराव / \(2.01001000100001\ldots\) without fixed repetition
D (5.75)
Explanation opens after your attempt
Correct Answer
C. \(2.01001000100001\ldots\) बिना निश्चित दोहराव / \(2.01001000100001\ldots\) without fixed repetition
Step 1
Concept
A non-terminating decimal without fixed repetition can be irrational. Terminating and recurring decimals are rational.
Step 2
Why this answer is correct
The correct answer is C. \(2.01001000100001\ldots\) बिना निश्चित दोहराव / \(2.01001000100001\ldots\) without fixed repetition. A non-terminating decimal without fixed repetition can be irrational. Terminating and recurring decimals are rational.
Step 3
Exam Tip
बिना निश्चित दोहराव वाला असांत दशमलव अपरिमेय हो सकता है। सांत और आवर्ती दशमलव परिमेय होते हैं।
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यदि \( \frac{p}{q} \) सरल रूप में है और \(q=2^3\times5^2\), तो दशमलव प्रसार कैसा होगा?
If \( \frac{p}{q} \) is in simplest form and \(q=2^3\times5^2\), 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 निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
B. सांत / Terminating
Step 1
Concept
The denominator has only the factors (2) and (5). Therefore, the decimal expansion will be terminating.
Step 2
Why this answer is correct
The correct answer is B. सांत / Terminating. The denominator has only the factors (2) and (5). Therefore, the decimal expansion will be terminating.
Step 3
Exam Tip
हर में केवल (2) और (5) के गुणनखंड हैं। इसलिए दशमलव प्रसार सांत होगा।
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यदि \( \frac{p}{q} \) सरल रूप में है और \(q=2^2\times3\times5\), तो दशमलव प्रसार कैसा होगा?
If \( \frac{p}{q} \) is in simplest form and \(q=2^2\times3\times5\), what type of decimal expansion will it have?
#number-systems
#decimal-representation
#prime-factor-test
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A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D हमेशा शून्य / Always zero
Explanation opens after your attempt
Correct Answer
B. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
The denominator has (3), 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 B. असांत आवर्ती / Non-terminating recurring. The denominator has (3), a factor other than (2) and (5). So the rational number will have a non-terminating recurring decimal.
Step 3
Exam Tip
हर में (3) है, जो (2) और (5) के अलावा गुणनखंड है। इसलिए परिमेय संख्या का दशमलव असांत आवर्ती होगा।
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दशमलव \(0.2\overline{7}\) किस रूप में लिखा जा सकता है?
How can the decimal \(0.2\overline{7}\) be written?
#number-systems
#decimal-representation
#bar-notation
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A \(0.2777\ldots\)
B \(0.272727\ldots\)
C \(0.2227\ldots\)
D (0.27)
Explanation opens after your attempt
Correct Answer
A. \(0.2777\ldots\)
Step 1
Concept
The bar is only over (7), so (7) repeats. Hence the number is \(0.2777\ldots\).
Step 2
Why this answer is correct
The correct answer is A. \(0.2777\ldots\). The bar is only over (7), so (7) repeats. Hence the number is \(0.2777\ldots\).
Step 3
Exam Tip
बार केवल (7) पर है, इसलिए (7) बार-बार दोहरता है। अतः संख्या \(0.2777\ldots\) है।
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(0.004) और (0.0004) में (0.004) कितने गुना है?
How many times is (0.004) of (0.0004)?
#number-systems
#decimal-representation
#decimal-comparison
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A (1) गुना / (1) time
B (10) गुना / (10) times
C (100) गुना / (100) times
D (1000) गुना / (1000) times
Explanation opens after your attempt
Correct Answer
B. (10) गुना / (10) times
Step 1
Concept
\(0.004\div0.0004=10\). The difference in decimal places shows the multiplication relation.
Step 2
Why this answer is correct
The correct answer is B. (10) गुना / (10) times. \(0.004\div0.0004=10\). The difference in decimal places shows the multiplication relation.
Step 3
Exam Tip
\(0.004\div0.0004=10\) है। दशमलव स्थानों का अंतर गुणन संबंध बताता है।
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भिन्न \( \frac{3}{32} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{3}{32} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.09375)
B (0.0932)
C (0.375)
D (0.0323)
Explanation opens after your attempt
Correct Answer
A. (0.09375)
Step 1
Concept
\(32\times3125=100000\), so \( \frac{3}{32}=\frac{9375}{100000}=0.09375 \). Converting the denominator into a power of (10) is useful.
Step 2
Why this answer is correct
The correct answer is A. (0.09375). \(32\times3125=100000\), so \( \frac{3}{32}=\frac{9375}{100000}=0.09375 \). Converting the denominator into a power of (10) is useful.
Step 3
Exam Tip
\(32\times3125=100000\), इसलिए \( \frac{3}{32}=\frac{9375}{100000}=0.09375 \) है। हर को (10) की घात में बदलना उपयोगी है।
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दशमलव (7.5408) में (4) का स्थानीय मान क्या है?
What is the place value of (4) in (7.5408)?
#number-systems
#decimal-representation
#place-value
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A \( \frac{4}{10} \)
B \( \frac{4}{100} \)
C \( \frac{4}{1000} \)
D \( \frac{4}{10000} \)
Explanation opens after your attempt
Correct Answer
B. \( \frac{4}{100} \)
Step 1
Concept
(4) is in the second place after the decimal point. The second decimal place is hundredths.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{4}{100} \). (4) is in the second place after the decimal point. The second decimal place is hundredths.
Step 3
Exam Tip
(4) दशमलव के बाद दूसरे स्थान पर है। दूसरा दशमलव स्थान सौवां होता है।
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दशमलव (0.09009) में पहले (9) का स्थानीय मान क्या है?
What is the place value of the first (9) in (0.09009)?
#number-systems
#decimal-representation
#place-value
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A \( \frac{9}{10} \)
B \( \frac{9}{100} \)
C \( \frac{9}{1000} \)
D \( \frac{9}{10000} \)
Explanation opens after your attempt
Correct Answer
B. \( \frac{9}{100} \)
Step 1
Concept
The first (9) is in the second place after the decimal point. So its place value is \( \frac{9}{100} \).
Step 2
Why this answer is correct
The correct answer is B. \( \frac{9}{100} \). The first (9) is in the second place after the decimal point. So its place value is \( \frac{9}{100} \).
Step 3
Exam Tip
पहला (9) दशमलव के बाद दूसरे स्थान पर है। इसलिए उसका स्थानीय मान \( \frac{9}{100} \) है।
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(2.375) को मिश्रित भिन्न में लिखने पर क्या मिलेगा?
What is obtained when (2.375) is written as a mixed fraction?
#number-systems
#decimal-representation
#mixed-fraction
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A \(2\frac{3}{8}\)
B \(2\frac{5}{8}\)
C \(2\frac{7}{8}\)
D \(3\frac{2}{8}\)
Explanation opens after your attempt
Correct Answer
A. \(2\frac{3}{8}\)
Step 1
Concept
\(0.375=\frac{3}{8}\), so \(2.375=2\frac{3}{8}\). First convert the decimal part into a fraction.
Step 2
Why this answer is correct
The correct answer is A. \(2\frac{3}{8}\). \(0.375=\frac{3}{8}\), so \(2.375=2\frac{3}{8}\). First convert the decimal part into a fraction.
Step 3
Exam Tip
\(0.375=\frac{3}{8}\), इसलिए \(2.375=2\frac{3}{8}\) है। पहले दशमलव भाग को भिन्न में बदलें।
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किस संख्या को (0.2), (0.02), (0.002) के बढ़ते क्रम में सबसे पहले रखा जाएगा?
Which number will be placed first in the ascending order of (0.2), (0.02), and (0.002)?
#number-systems
#decimal-representation
#ascending-order
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A (0.2)
B (0.02)
C (0.002)
D तीनों बराबर हैं / All three are equal
Explanation opens after your attempt
Correct Answer
C. (0.002)
Step 1
Concept
The smallest is (0.002). The position of zero changes the value of a decimal number.
Step 2
Why this answer is correct
The correct answer is C. (0.002). The smallest is (0.002). The position of zero changes the value of a decimal number.
Step 3
Exam Tip
सबसे छोटा (0.002) है। दशमलव में शून्य का स्थान संख्या का मान बदल देता है।
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दशमलव (0.00125) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.00125) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{1}{800} \)
B \( \frac{1}{80} \)
C \( \frac{1}{8} \)
D \( \frac{125}{1000} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{1}{800} \)
Step 1
Concept
\(0.00125=\frac{125}{100000}=\frac{1}{800}\). Count decimal places to write the correct denominator.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{1}{800} \). \(0.00125=\frac{125}{100000}=\frac{1}{800}\). Count decimal places to write the correct denominator.
Step 3
Exam Tip
\(0.00125=\frac{125}{100000}=\frac{1}{800}\) है। दशमलव स्थान गिनकर सही हर लिखें।
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कौन-सा दशमलव \( \frac{7}{9} \) के बराबर है?
Which decimal is equal to \( \frac{7}{9} \)?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.777\ldots\)
B (0.79)
C (0.709)
D \(0.7979\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(0.777\ldots\)
Step 1
Concept
\( \frac{7}{9}=0.777\ldots \). For \( \frac{n}{9} \), the same digit repeats.
Step 2
Why this answer is correct
The correct answer is A. \(0.777\ldots\). \( \frac{7}{9}=0.777\ldots \). For \( \frac{n}{9} \), the same digit repeats.
Step 3
Exam Tip
\( \frac{7}{9}=0.777\ldots \) है। \( \frac{n}{9} \) के लिए वही अंक बार-बार आता है।
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कौन-सा दशमलव (0.7) से छोटा लेकिन (0.69) से बड़ा है?
Which decimal is less than (0.7) but greater than (0.69)?
#number-systems
#decimal-representation
#between-decimals
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A (0.689)
B (0.700)
C (0.695)
D (0.609)
Explanation opens after your attempt
Correct Answer
C. (0.695)
Step 1
Concept
(0.695) is greater than (0.690) and less than (0.700). For a number between two limits, write both limits up to equal decimal places.
Step 2
Why this answer is correct
The correct answer is C. (0.695). (0.695) is greater than (0.690) and less than (0.700). For a number between two limits, write both limits up to equal decimal places.
Step 3
Exam Tip
(0.695), (0.690) से बड़ा और (0.700) से छोटा है। बीच की संख्या के लिए दोनों सीमाओं को समान दशमलव स्थान तक लिखें।
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कौन-सा दशमलव (0.1250) के बराबर नहीं है?
Which decimal is not equal to (0.1250)?
#number-systems
#decimal-representation
#equivalent-decimals
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A (0.125)
B (0.12500)
C (0.0125)
D (0.125000)
Explanation opens after your attempt
Correct Answer
C. (0.0125)
Step 1
Concept
(0.0125) is smaller than (0.1250) because the place of digits changes. Only adding or removing zeros at the end does not change value.
Step 2
Why this answer is correct
The correct answer is C. (0.0125). (0.0125) is smaller than (0.1250) because the place of digits changes. Only adding or removing zeros at the end does not change value.
Step 3
Exam Tip
(0.0125), (0.1250) से छोटा है क्योंकि अंक का स्थान बदल गया है। केवल अंत में शून्य जोड़ने या हटाने से मान नहीं बदलता।
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दशमलव \(4.505505505\ldots\) का आवर्ती भाग क्या है?
What is the recurring part of \(4.505505505\ldots\)?
#number-systems
#decimal-representation
#repeating-block
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A (50)
B (05)
C (505)
D (550)
Explanation opens after your attempt
Step 1
Concept
The block (505) repeats continuously. The bar is placed only over the recurring part.
Step 2
Why this answer is correct
The correct answer is C. (505). The block (505) repeats continuously. The bar is placed only over the recurring part.
Step 3
Exam Tip
(505) का समूह लगातार दोहर रहा है। आवर्ती भाग पर ही बार लगाया जाता है।
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सरल रूप में \( \frac{18}{75} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{18}{75} \) 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 निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
B. सांत / Terminating
Step 1
Concept
\( \frac{18}{75}=\frac{6}{25} \) and \(25=5^2\). Therefore, its decimal expansion will be terminating.
Step 2
Why this answer is correct
The correct answer is B. सांत / Terminating. \( \frac{18}{75}=\frac{6}{25} \) and \(25=5^2\). Therefore, its decimal expansion will be terminating.
Step 3
Exam Tip
\( \frac{18}{75}=\frac{6}{25} \) और \(25=5^2\) है। इसलिए इसका दशमलव प्रसार सांत होगा।
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सरल रूप में \( \frac{35}{42} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{35}{42} \) 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
B. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
\( \frac{35}{42}=\frac{5}{6} \) and \(6=2\times3\). Since the denominator has (3), the decimal will be non-terminating recurring.
Step 2
Why this answer is correct
The correct answer is B. असांत आवर्ती / Non-terminating recurring. \( \frac{35}{42}=\frac{5}{6} \) and \(6=2\times3\). Since the denominator has (3), the decimal will be non-terminating recurring.
Step 3
Exam Tip
\( \frac{35}{42}=\frac{5}{6} \) और \(6=2\times3\) है। हर में (3) होने से दशमलव असांत आवर्ती होगा।
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भिन्न \( \frac{43}{160} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{43}{160} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.26875)
B (0.43160)
C (0.6875)
D (2.6875)
Explanation opens after your attempt
Correct Answer
A. (0.26875)
Step 1
Concept
\(160\times625=100000\), so \( \frac{43}{160}=\frac{26875}{100000}=0.26875 \). Making the denominator a power of (10) gives an exact answer.
Step 2
Why this answer is correct
The correct answer is A. (0.26875). \(160\times625=100000\), so \( \frac{43}{160}=\frac{26875}{100000}=0.26875 \). Making the denominator a power of (10) gives an exact answer.
Step 3
Exam Tip
\(160\times625=100000\), इसलिए \( \frac{43}{160}=\frac{26875}{100000}=0.26875 \) है। हर को (10) की घात बनाने से उत्तर सटीक मिलता है।
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दशमलव (0.0064) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.0064) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{64}{1000} \)
B \( \frac{16}{2500} \)
C \( \frac{4}{625} \)
D \( \frac{8}{125} \)
Explanation opens after your attempt
Correct Answer
C. \( \frac{4}{625} \)
Step 1
Concept
\(0.0064=\frac{64}{10000}=\frac{4}{625}\). Count decimal places to write the denominator and then simplify the fraction.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{4}{625} \). \(0.0064=\frac{64}{10000}=\frac{4}{625}\). Count decimal places to write the denominator and then simplify the fraction.
Step 3
Exam Tip
\(0.0064=\frac{64}{10000}=\frac{4}{625}\) है। दशमलव स्थान गिनकर हर लिखें और फिर भिन्न को सरल करें।
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सरल रूप में \( \frac{27}{90} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{27}{90} \) 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
\( \frac{27}{90}=\frac{3}{10} \), and the denominator has only factors (2) and (5). Therefore, its decimal expansion will be terminating.
Step 2
Why this answer is correct
The correct answer is B. सांत / Terminating. \( \frac{27}{90}=\frac{3}{10} \), and the denominator has only factors (2) and (5). Therefore, its decimal expansion will be terminating.
Step 3
Exam Tip
\( \frac{27}{90}=\frac{3}{10} \) और हर में केवल (2) तथा (5) के गुणनखंड हैं। इसलिए इसका दशमलव प्रसार सांत होगा।
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दशमलव \(0.0131313\ldots\) का सही बार संकेतन कौन-सा है?
Which is the correct bar notation of \(0.0131313\ldots\)?
#number-systems
#decimal-representation
#bar-notation
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A \(0.\overline{013}\)
B \(0.0\overline{13}\)
C \(0.\overline{13}\)
D \(0.01\overline{3}\)
Explanation opens after your attempt
Correct Answer
B. \(0.0\overline{13}\)
Step 1
Concept
After the first (0), the block (13) repeats again and again. The bar should be placed only over the repeating part.
Step 2
Why this answer is correct
The correct answer is B. \(0.0\overline{13}\). After the first (0), the block (13) repeats again and again. The bar should be placed only over the repeating part.
Step 3
Exam Tip
पहले (0) के बाद (13) का समूह बार-बार दोहरता है। बार केवल दोहराने वाले भाग पर लगाना चाहिए।
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(2.304), (2.34), (2.034), (2.043) का घटते क्रम कौन-सा है?
What is the descending order of (2.304), (2.34), (2.034), and (2.043)?
#number-systems
#decimal-representation
#descending-order
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A (2.34>2.304>2.043>2.034)
B (2.304>2.34>2.043>2.034)
C (2.034>2.043>2.304>2.34)
D (2.34>2.043>2.304>2.034)
Explanation opens after your attempt
Correct Answer
A. (2.34>2.304>2.043>2.034)
Step 1
Concept
(2.34=2.340), so it is the greatest and (2.034) is the smallest. Write all decimals up to equal places for comparison.
Step 2
Why this answer is correct
The correct answer is A. (2.34>2.304>2.043>2.034). (2.34=2.340), so it is the greatest and (2.034) is the smallest. Write all decimals up to equal places for comparison.
Step 3
Exam Tip
(2.34=2.340), इसलिए यह सबसे बड़ा है और (2.034) सबसे छोटा है। तुलना में सभी दशमलवों को समान स्थान तक लिखें।
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यदि (100x=45.6), तो (x) का मान क्या होगा?
If (100x=45.6), what is the value of (x)?
#number-systems
#decimal-representation
#decimal-division
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A (4560)
B (4.56)
C (0.456)
D (0.0456)
Explanation opens after your attempt
Correct Answer
C. (0.456)
Step 1
Concept
\(x=45.6\div100=0.456\). On dividing by (100), the decimal point moves two places to the left.
Step 2
Why this answer is correct
The correct answer is C. (0.456). \(x=45.6\div100=0.456\). On dividing by (100), the decimal point moves two places to the left.
Step 3
Exam Tip
\(x=45.6\div100=0.456\) है। (100) से भाग देने पर दशमलव बिंदु दो स्थान बाईं ओर जाता है।
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