भिन्न \( \frac{17}{200} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{17}{200} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.085)
B (0.017)
C (0.85)
D (1.70)
Explanation opens after your attempt
Correct Answer
A. (0.085)
Step 1
Concept
\( \frac{17}{200}=\frac{85}{1000}=0.085 \). Convert the denominator into a power of (10) to find the decimal.
Step 2
Why this answer is correct
The correct answer is A. (0.085). \( \frac{17}{200}=\frac{85}{1000}=0.085 \). Convert the denominator into a power of (10) to find the decimal.
Step 3
Exam Tip
\( \frac{17}{200}=\frac{85}{1000}=0.085 \) है। हर को (10) की घात में बदलकर दशमलव निकालें।
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भिन्न \( \frac{31}{400} \) का दशमलव रूप कौन-सा है?
Which is the decimal form of \( \frac{31}{400} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.0314)
B (0.0775)
C (0.775)
D (0.40031)
Explanation opens after your attempt
Correct Answer
B. (0.0775)
Step 1
Concept
\(400\times25=10000\), so \( \frac{31}{400}=\frac{775}{10000}=0.0775 \). Making the denominator a power of (10) is useful.
Step 2
Why this answer is correct
The correct answer is B. (0.0775). \(400\times25=10000\), so \( \frac{31}{400}=\frac{775}{10000}=0.0775 \). Making the denominator a power of (10) is useful.
Step 3
Exam Tip
\(400\times25=10000\), इसलिए \( \frac{31}{400}=\frac{775}{10000}=0.0775 \) है। हर को (10) की घात बनाना उपयोगी है।
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दशमलव (0.21875) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.21875) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{21}{875} \)
B \( \frac{175}{800} \)
C \( \frac{7}{32} \)
D \( \frac{21875}{1000} \)
Explanation opens after your attempt
Correct Answer
C. \( \frac{7}{32} \)
Step 1
Concept
\(0.21875=\frac{21875}{100000}=\frac{7}{32}\). Convert the decimal to a fraction and reduce it to simplest form.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{7}{32} \). \(0.21875=\frac{21875}{100000}=\frac{7}{32}\). Convert the decimal to a fraction and reduce it to simplest form.
Step 3
Exam Tip
\(0.21875=\frac{21875}{100000}=\frac{7}{32}\) है। दशमलव को भिन्न में बदलकर सबसे सरल रूप तक घटाएं।
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दशमलव (1.0625) को अनुचित भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (1.0625) is converted into an improper fraction?
#number-systems
#decimal-representation
#improper-fraction
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A \( \frac{16}{17} \)
B \( \frac{10625}{1000} \)
C \( \frac{9}{8} \)
D \( \frac{17}{16} \)
Explanation opens after your attempt
Correct Answer
D. \( \frac{17}{16} \)
Step 1
Concept
\(1.0625=\frac{10625}{10000}=\frac{17}{16}\). Keep the final improper fraction in simplest form.
Step 2
Why this answer is correct
The correct answer is D. \( \frac{17}{16} \). \(1.0625=\frac{10625}{10000}=\frac{17}{16}\). Keep the final improper fraction in simplest form.
Step 3
Exam Tip
\(1.0625=\frac{10625}{10000}=\frac{17}{16}\) है। अनुचित भिन्न में बदलते समय अंतिम उत्तर सरल रखें।
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दशमलव (6.3042) का विस्तारित रूप कौन-सा है?
Which is the expanded form of (6.3042)?
#number-systems
#decimal-representation
#expanded-form
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A \(6+\frac{3}{10}+\frac{4}{1000}+\frac{2}{10000}\)
B \(6+\frac{3}{100}+\frac{4}{1000}+\frac{2}{10000}\)
C \(6+\frac{30}{10}+\frac{42}{100}\)
D \(63+\frac{42}{10000}\)
Explanation opens after your attempt
Correct Answer
A. \(6+\frac{3}{10}+\frac{4}{1000}+\frac{2}{10000}\)
Step 1
Concept
(3) is in tenths, (4) is in thousandths, and (2) is in ten-thousandths. A zero place need not be written in expansion.
Step 2
Why this answer is correct
The correct answer is A. \(6+\frac{3}{10}+\frac{4}{1000}+\frac{2}{10000}\). (3) is in tenths, (4) is in thousandths, and (2) is in ten-thousandths. A zero place need not be written in expansion.
Step 3
Exam Tip
(3) दसवें, (4) हजारवें और (2) दस हजारवें स्थान पर है। शून्य वाले स्थान का मान लिखना आवश्यक नहीं होता।
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दशमलव (0.50709) में (9) का स्थानीय मान क्या है?
What is the place value of (9) in (0.50709)?
#number-systems
#decimal-representation
#place-value
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A \( \frac{9}{1000} \)
B \( \frac{9}{10000} \)
C \( \frac{9}{100000} \)
D \( \frac{9}{100} \)
Explanation opens after your attempt
Correct Answer
C. \( \frac{9}{100000} \)
Step 1
Concept
(9) is in the fifth place after the decimal point. The fifth decimal place is hundred-thousandths.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{9}{100000} \). (9) is in the fifth place after the decimal point. The fifth decimal place is hundred-thousandths.
Step 3
Exam Tip
(9) दशमलव के बाद पांचवें स्थान पर है। पांचवां दशमलव स्थान लाखवां होता है।
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दशमलव \(0.23131313\ldots\) में आवर्ती भाग कौन-सा है?
What is the recurring part in \(0.23131313\ldots\)?
#number-systems
#decimal-representation
#repeating-block
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A (23)
B (31)
C (131)
D (13)
Explanation opens after your attempt
Step 1
Concept
After the first (23), the block (13) repeats again and again. The recurring part is the smallest repeating block.
Step 2
Why this answer is correct
The correct answer is D. (13). After the first (23), the block (13) repeats again and again. The recurring part is the smallest repeating block.
Step 3
Exam Tip
पहले (23) के बाद (13) का समूह बार-बार दोहरता है। आवर्ती भाग सबसे छोटा दोहराने वाला समूह होता है।
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दशमलव \(3.0454545\ldots\) का सही बार संकेतन कौन-सा है?
Which is the correct bar notation of \(3.0454545\ldots\)?
#number-systems
#decimal-representation
#bar-notation
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A \(3.0\overline{45}\)
B \(3.\overline{045}\)
C \(3.04\overline{5}\)
D \(3.\overline{45}\)
Explanation opens after your attempt
Correct Answer
A. \(3.0\overline{45}\)
Step 1
Concept
After the first (0) in the decimal part, (45) repeats. The bar should be placed only over the recurring part.
Step 2
Why this answer is correct
The correct answer is A. \(3.0\overline{45}\). After the first (0) in the decimal part, (45) repeats. The bar should be placed only over the recurring part.
Step 3
Exam Tip
दशमलव में पहले (0) के बाद (45) दोहरता है। बार केवल आवर्ती भाग पर लगाना चाहिए।
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सरल रूप में \( \frac{19}{96} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{19}{96} \) 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 केवल पूर्णांक / Integer only
Explanation opens after your attempt
Correct Answer
B. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
\(96=2^5\times3\) also has (3). So this rational number will give a non-terminating recurring decimal.
Step 2
Why this answer is correct
The correct answer is B. असांत आवर्ती / Non-terminating recurring. \(96=2^5\times3\) also has (3). So this rational number will give a non-terminating recurring decimal.
Step 3
Exam Tip
\(96=2^5\times3\) में (3) भी है। इसलिए यह परिमेय संख्या असांत आवर्ती दशमलव देगी।
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सरल रूप में \( \frac{27}{320} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{27}{320} \) have?
#number-systems
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#terminating-test
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A असांत आवर्ती / Non-terminating recurring
B असांत अनावर्ती / Non-terminating non-recurring
C सांत / Terminating
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
C. सांत / Terminating
Step 1
Concept
\(320=2^6\times5\), so the denominator has only (2) and (5). Such a denominator gives a terminating decimal.
Step 2
Why this answer is correct
The correct answer is C. सांत / Terminating. \(320=2^6\times5\), so the denominator has only (2) and (5). Such a denominator gives a terminating decimal.
Step 3
Exam Tip
\(320=2^6\times5\) है, इसलिए हर में केवल (2) और (5) हैं। ऐसा हर सांत दशमलव देता है।
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(0.625), (0.0625), (0.6025), (0.6205) में सबसे बड़ी संख्या कौन-सी है?
Among (0.625), (0.0625), (0.6025), and (0.6205), which is the greatest number?
#number-systems
#decimal-representation
#compare-decimals
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A (0.6025)
B (0.625)
C (0.6205)
D (0.0625)
Explanation opens after your attempt
Correct Answer
B. (0.625)
Step 1
Concept
(0.6250) is greater than (0.6205), (0.6025), and (0.0625). Write all decimals up to equal places for comparison.
Step 2
Why this answer is correct
The correct answer is B. (0.625). (0.6250) is greater than (0.6205), (0.6025), and (0.0625). Write all decimals up to equal places for comparison.
Step 3
Exam Tip
(0.6250), (0.6205), (0.6025) और (0.0625) से बड़ा है। तुलना के लिए सभी दशमलवों को समान स्थान तक लिखें।
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(1.03), (1.003), (1.0303), (1.300) का बढ़ता क्रम कौन-सा है?
What is the ascending order of (1.03), (1.003), (1.0303), and (1.300)?
#number-systems
#decimal-representation
#ascending-order
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A (1.003<1.03<1.0303<1.300)
B (1.03<1.003<1.0303<1.300)
C (1.300<1.0303<1.03<1.003)
D (1.003<1.0303<1.03<1.300)
Explanation opens after your attempt
Correct Answer
A. (1.003<1.03<1.0303<1.300)
Step 1
Concept
(1.03=1.0300), so (1.0303) is slightly greater. Arrange decimals after writing equal places.
Step 2
Why this answer is correct
The correct answer is A. (1.003<1.03<1.0303<1.300). (1.03=1.0300), so (1.0303) is slightly greater. Arrange decimals after writing equal places.
Step 3
Exam Tip
(1.03=1.0300), इसलिए (1.0303) इससे थोड़ा बड़ा है। दशमलवों को समान स्थान तक लिखकर क्रम लगाएं।
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कौन-सी संख्या (0.718) और (0.719) के बीच है?
Which number lies between (0.718) and (0.719)?
#number-systems
#decimal-representation
#between-decimals
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A (0.7179)
B (0.7190)
C (0.7185)
D (0.7200)
Explanation opens after your attempt
Correct Answer
C. (0.7185)
Step 1
Concept
(0.7185) is greater than (0.7180) and less than (0.7190). Make decimal places equal while finding a number between two decimals.
Step 2
Why this answer is correct
The correct answer is C. (0.7185). (0.7185) is greater than (0.7180) and less than (0.7190). Make decimal places equal while finding a number between two decimals.
Step 3
Exam Tip
(0.7185), (0.7180) से बड़ा और (0.7190) से छोटा है। बीच की संख्या खोजते समय दशमलव स्थान समान करें।
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दशमलव (0.00072) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.00072) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{72}{1000} \)
B \( \frac{18}{25000} \)
C \( \frac{9}{12500} \)
D \( \frac{72}{10000} \)
Explanation opens after your attempt
Correct Answer
C. \( \frac{9}{12500} \)
Step 1
Concept
\(0.00072=\frac{72}{100000}=\frac{9}{12500}\). For five decimal places, use denominator (100000).
Step 2
Why this answer is correct
The correct answer is C. \( \frac{9}{12500} \). \(0.00072=\frac{72}{100000}=\frac{9}{12500}\). For five decimal places, use denominator (100000).
Step 3
Exam Tip
\(0.00072=\frac{72}{100000}=\frac{9}{12500}\) है। पांच दशमलव स्थान होने पर हर (100000) लें।
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दशमलव (0.875) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.875) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{7}{8} \)
B \( \frac{5}{8} \)
C \( \frac{875}{100} \)
D \( \frac{35}{40} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{7}{8} \)
Step 1
Concept
\(0.875=\frac{875}{1000}=\frac{7}{8}\). Do not forget to simplify the fraction in the final form.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{7}{8} \). \(0.875=\frac{875}{1000}=\frac{7}{8}\). Do not forget to simplify the fraction in the final form.
Step 3
Exam Tip
\(0.875=\frac{875}{1000}=\frac{7}{8}\) है। भिन्न को अंतिम रूप में सरल करना न भूलें।
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भिन्न \( \frac{7}{18} \) का दशमलव प्रसार कौन-सा है?
Which is the decimal expansion of \( \frac{7}{18} \)?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.71818\ldots\)
B \(0.3888\ldots\)
C \(0.3939\ldots\)
D (0.78)
Explanation opens after your attempt
Correct Answer
B. \(0.3888\ldots\)
Step 1
Concept
\(7\div18=0.3888\ldots\). The digit that repeats during division is the recurring part.
Step 2
Why this answer is correct
The correct answer is B. \(0.3888\ldots\). \(7\div18=0.3888\ldots\). The digit that repeats during division is the recurring part.
Step 3
Exam Tip
\(7\div18=0.3888\ldots\) होता है। भाग देने पर जो अंक बार-बार आए, वही आवर्ती भाग है।
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भिन्न \( \frac{8}{33} \) का दशमलव प्रसार कौन-सा है?
Which is the decimal expansion of \( \frac{8}{33} \)?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.242424\ldots\)
B \(0.83333\ldots\)
C \(0.0808\ldots\)
D \(0.2433\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(0.242424\ldots\)
Step 1
Concept
\(8\div33=0.242424\ldots\). Here the block (24) repeats continuously.
Step 2
Why this answer is correct
The correct answer is A. \(0.242424\ldots\). \(8\div33=0.242424\ldots\). Here the block (24) repeats continuously.
Step 3
Exam Tip
\(8\div33=0.242424\ldots\) होता है। यहां (24) का समूह लगातार दोहरता है।
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दशमलव \(0.006006006\ldots\) का सही बार संकेतन कौन-सा है?
Which is the correct bar notation of \(0.006006006\ldots\)?
#number-systems
#decimal-representation
#bar-notation
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A \(0.0\overline{06}\)
B \(0.\overline{006}\)
C \(0.00\overline{6}\)
D \(0.\overline{6}\)
Explanation opens after your attempt
Correct Answer
B. \(0.\overline{006}\)
Step 1
Concept
The whole block (006) repeats again and again. So the bar is placed over the whole (006).
Step 2
Why this answer is correct
The correct answer is B. \(0.\overline{006}\). The whole block (006) repeats again and again. So the bar is placed over the whole (006).
Step 3
Exam Tip
(006) का पूरा समूह बार-बार दोहरता है। इसलिए बार पूरे (006) पर लगेगा।
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दशमलव \(5.1020202\ldots\) का आवर्ती भाग क्या है?
What is the recurring part of \(5.1020202\ldots\)?
#number-systems
#decimal-representation
#repeating-block
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A (10)
B (02)
C (20)
D (102)
Explanation opens after your attempt
Step 1
Concept
After the first (10), the block (02), not (20), repeats. Identify the recurring part with its order.
Step 2
Why this answer is correct
The correct answer is B. (02). After the first (10), the block (02), not (20), repeats. Identify the recurring part with its order.
Step 3
Exam Tip
पहले (10) के बाद (20) नहीं बल्कि (02) का समूह दोहरता है। आवर्ती भाग को क्रम सहित पहचानें।
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दशमलव \(2.7182818284\ldots\) बिना निश्चित दोहराव किस प्रकार का है?
What type of decimal is \(2.7182818284\ldots\) without fixed repetition?
#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 परिमेय पूर्णांक / Rational integer
Explanation opens after your attempt
Correct Answer
C. असांत अनावर्ती / Non-terminating non-recurring
Step 1
Concept
It does not terminate and has no fixed recurring part. Such a decimal is called non-terminating non-recurring.
Step 2
Why this answer is correct
The correct answer is C. असांत अनावर्ती / Non-terminating non-recurring. It does not terminate and has no fixed recurring part. Such a decimal is called non-terminating non-recurring.
Step 3
Exam Tip
यह समाप्त नहीं होता और इसमें निश्चित आवर्ती भाग भी नहीं है। ऐसा दशमलव असांत अनावर्ती कहलाता है।
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यदि \( \frac{p}{q} \) सरल रूप में है और \(q=2^2\times5^3\times7\), तो दशमलव प्रसार कैसा होगा?
If \( \frac{p}{q} \) is in simplest form and \(q=2^2\times5^3\times7\), 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 (7), 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 (7), a factor other than (2) and (5). So the rational number will have a non-terminating recurring decimal.
Step 3
Exam Tip
हर में (7) है, जो (2) और (5) के अलावा गुणनखंड है। इसलिए परिमेय संख्या का दशमलव असांत आवर्ती होगा।
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यदि \( \frac{p}{q} \) सरल रूप में है और \(q=2^6\times5\), तो दशमलव प्रसार कैसा होगा?
If \( \frac{p}{q} \) is in simplest form and \(q=2^6\times5\), 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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(0.84) को \( \frac{21}{25} \) से तुलना करने पर सही कथन कौन-सा है?
Which statement is correct when (0.84) is compared with \( \frac{21}{25} \)?
#number-systems
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#compare-fraction-decimal
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A \(0.84<\frac{21}{25}\)
B \(0.84>\frac{21}{25}\)
C \(0.84=\frac{21}{25}\)
D तुलना नहीं हो सकती / Cannot be compared
Explanation opens after your attempt
Correct Answer
C. \(0.84=\frac{21}{25}\)
Step 1
Concept
\( \frac{21}{25}=\frac{84}{100}=0.84 \). Convert the fraction into decimal to compare.
Step 2
Why this answer is correct
The correct answer is C. \(0.84=\frac{21}{25}\). \( \frac{21}{25}=\frac{84}{100}=0.84 \). Convert the fraction into decimal to compare.
Step 3
Exam Tip
\( \frac{21}{25}=\frac{84}{100}=0.84 \) है। भिन्न को दशमलव में बदलकर तुलना करें।
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भिन्न \( \frac{9}{16} \) और दशमलव (0.57) में कौन बड़ा है?
Which is greater between \( \frac{9}{16} \) and (0.57)?
#number-systems
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#compare-fraction-decimal
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A \( \frac{9}{16} \)
B (0.57)
C दोनों बराबर हैं / Both are equal
D तुलना नहीं हो सकती / Cannot be compared
Explanation opens after your attempt
Step 1
Concept
\( \frac{9}{16}=0.5625 \), which is less than (0.57). Convert the fraction to a decimal before comparison.
Step 2
Why this answer is correct
The correct answer is B. (0.57). \( \frac{9}{16}=0.5625 \), which is less than (0.57). Convert the fraction to a decimal before comparison.
Step 3
Exam Tip
\( \frac{9}{16}=0.5625 \), जो (0.57) से छोटा है। तुलना से पहले भिन्न को दशमलव में बदलें।
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(0.075) को प्रतिशत में बदलने पर क्या मिलेगा?
What is obtained by converting (0.075) into a percentage?
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#decimal-percent
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A (75%)
B (0.75%)
C (7.5%)
D (0.075%)
Explanation opens after your attempt
Step 1
Concept
\(0.075\times100=7.5\), so it is (7.5%). Multiply by (100) to convert into percentage.
Step 2
Why this answer is correct
The correct answer is C. (7.5%). \(0.075\times100=7.5\), so it is (7.5%). Multiply by (100) to convert into percentage.
Step 3
Exam Tip
\(0.075\times100=7.5\), इसलिए (7.5%) है। प्रतिशत में बदलने के लिए (100) से गुणा करें।
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(12.06) को (1000) से भाग देने पर क्या मिलेगा?
What is obtained by dividing (12.06) by (1000)?
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A (1.206)
B (0.1206)
C (0.01206)
D (12060)
Explanation opens after your attempt
Correct Answer
C. (0.01206)
Step 1
Concept
\(12.06\div1000=0.01206\). On dividing by (1000), the decimal point moves three places to the left.
Step 2
Why this answer is correct
The correct answer is C. (0.01206). \(12.06\div1000=0.01206\). On dividing by (1000), the decimal point moves three places to the left.
Step 3
Exam Tip
\(12.06\div1000=0.01206\) है। (1000) से भाग देने पर दशमलव बिंदु तीन स्थान बाईं ओर जाता है।
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\(0.48\div0.006\) का मान क्या है?
What is the value of \(0.48\div0.006\)?
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A (8)
B (80)
C (0.8)
D (800)
Explanation opens after your attempt
Step 1
Concept
Multiplying both numbers by (1000) gives \(480\div6=80\). Multiplying both parts of a division by the same number does not change the quotient.
Step 2
Why this answer is correct
The correct answer is B. (80). Multiplying both numbers by (1000) gives \(480\div6=80\). Multiplying both parts of a division by the same number does not change the quotient.
Step 3
Exam Tip
दोनों संख्याओं को (1000) से गुणा करने पर \(480\div6=80\) मिलता है। भाग में दोनों को समान संख्या से गुणा करने पर भागफल नहीं बदलता।
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(2.75+0.0875) का मान क्या है?
What is the value of (2.75+0.0875)?
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#decimal-addition
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A (2.8375)
B (2.7625)
C (2.8750)
D (3.625)
Explanation opens after your attempt
Correct Answer
A. (2.8375)
Step 1
Concept
(2.75=2.7500), so (2.7500+0.0875=2.8375). Align decimal points while adding.
Step 2
Why this answer is correct
The correct answer is A. (2.8375). (2.75=2.7500), so (2.7500+0.0875=2.8375). Align decimal points while adding.
Step 3
Exam Tip
(2.75=2.7500), इसलिए (2.7500+0.0875=2.8375) है। जोड़ते समय दशमलव बिंदु एक सीध में रखें।
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(4.125-1.0625) का मान क्या है?
What is the value of (4.125-1.0625)?
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#decimal-subtraction
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A (3.1875)
B (3.0625)
C (3.1250)
D (2.9375)
Explanation opens after your attempt
Correct Answer
B. (3.0625)
Step 1
Concept
(4.125=4.1250), so (4.1250-1.0625=3.0625). Add zeros in empty decimal places while subtracting.
Step 2
Why this answer is correct
The correct answer is B. (3.0625). (4.125=4.1250), so (4.1250-1.0625=3.0625). Add zeros in empty decimal places while subtracting.
Step 3
Exam Tip
(4.125=4.1250), इसलिए (4.1250-1.0625=3.0625) है। घटाते समय खाली दशमलव स्थानों में शून्य लगाएं।
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दशमलव (8.040) किसके बराबर है?
The decimal (8.040) is equal to which of the following?
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A (8.4)
B (8.004)
C (8.04)
D (80.40)
Explanation opens after your attempt
Step 1
Concept
A zero at the end of a decimal does not change the value. Therefore, (8.040=8.04).
Step 2
Why this answer is correct
The correct answer is C. (8.04). A zero at the end of a decimal does not change the value. Therefore, (8.040=8.04).
Step 3
Exam Tip
दशमलव के अंत का शून्य मान नहीं बदलता। इसलिए (8.040=8.04) है।
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कौन-सा दशमलव (0.0500) के बराबर नहीं है?
Which decimal is not equal to (0.0500)?
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A (0.05)
B (0.050)
C (0.500)
D (0.05000)
Explanation opens after your attempt
Correct Answer
C. (0.500)
Step 1
Concept
(0.500) is greater than (0.0500) because the place of (5) has changed. Only adding or removing ending zeros does not change value.
Step 2
Why this answer is correct
The correct answer is C. (0.500). (0.500) is greater than (0.0500) because the place of (5) has changed. Only adding or removing ending zeros does not change value.
Step 3
Exam Tip
(0.500), (0.0500) से बड़ा है क्योंकि (5) का स्थान बदल गया है। केवल अंत में शून्य जोड़ने या हटाने से मान नहीं बदलता।
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किस विकल्प में सभी संख्याएं परिमेय हैं?
In which option are all numbers rational?
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A (0.125), \(0.\overline{7}\), \(2.3434\ldots\)
B \(0.1010010001\ldots\), (0.25), (1.5)
C \(3.1415926\ldots\) बिना दोहराव, (0.5), (2.75) / \(3.1415926\ldots\) without repetition, (0.5), (2.75)
D \(1.010010001\ldots\), (4.2), (5.6)
Explanation opens after your attempt
Correct Answer
A. (0.125), \(0.\overline{7}\), \(2.3434\ldots\)
Step 1
Concept
Terminating and non-terminating recurring decimals are rational. All numbers in the first option are of these types.
Step 2
Why this answer is correct
The correct answer is A. (0.125), \(0.\overline{7}\), \(2.3434\ldots\). Terminating and non-terminating recurring decimals are rational. All numbers in the first option are of these types.
Step 3
Exam Tip
सांत और असांत आवर्ती दशमलव परिमेय होते हैं। पहले विकल्प में सभी संख्याएं इसी प्रकार की हैं।
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कौन-सा दशमलव अपरिमेय संख्या का रूप हो सकता है?
Which decimal can be the form of an irrational number?
#number-systems
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#irrational-decimal
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A \(0.272727\ldots\)
B (4.625)
C \(1.7320508\ldots\) बिना निश्चित दोहराव / \(1.7320508\ldots\) without fixed repetition
D \(6.\overline{04}\)
Explanation opens after your attempt
Correct Answer
C. \(1.7320508\ldots\) बिना निश्चित दोहराव / \(1.7320508\ldots\) without fixed repetition
Step 1
Concept
A non-terminating decimal without fixed repetition can be the form of an irrational number. Terminating and recurring decimals are rational.
Step 2
Why this answer is correct
The correct answer is C. \(1.7320508\ldots\) बिना निश्चित दोहराव / \(1.7320508\ldots\) without fixed repetition. A non-terminating decimal without fixed repetition can be the form of an irrational number. Terminating and recurring decimals are rational.
Step 3
Exam Tip
बिना निश्चित दोहराव वाला असांत दशमलव अपरिमेय संख्या का रूप हो सकता है। सांत और आवर्ती दशमलव परिमेय होते हैं।
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यदि (x=0.409) और (y=0.49), तो कौन-सा संबंध सही है?
If (x=0.409) and (y=0.49), which relation is correct?
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A (x>y)
B (x=y)
C (x<y)
D (y=0)
Explanation opens after your attempt
Step 1
Concept
(0.49=0.490), which is greater than (0.409). Write equal decimal places for comparison.
Step 2
Why this answer is correct
The correct answer is C. (x<y). (0.49=0.490), which is greater than (0.409). Write equal decimal places for comparison.
Step 3
Exam Tip
(0.49=0.490), जो (0.409) से बड़ा है। तुलना के लिए दशमलव स्थान समान लिखें।
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यदि (0.6a3<0.653), तो अंक (a) का सबसे बड़ा मान क्या हो सकता है?
If (0.6a3<0.653), what can be the greatest value of digit (a)?
#number-systems
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The tenths digits are equal and the hundredths digit must satisfy (a<5). So the greatest value is (4).
Step 2
Why this answer is correct
The correct answer is B. (4). The tenths digits are equal and the hundredths digit must satisfy (a<5). So the greatest value is (4).
Step 3
Exam Tip
दसवें स्थान समान हैं और सौवें स्थान पर (a<5) होना चाहिए। इसलिए सबसे बड़ा मान (4) है।
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यदि (100x=3.75), तो (x) का मान क्या है?
If (100x=3.75), what is the value of (x)?
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A (375)
B (0.375)
C (0.0375)
D (37.5)
Explanation opens after your attempt
Correct Answer
C. (0.0375)
Step 1
Concept
\(x=3.75\div100=0.0375\). 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. (0.0375). \(x=3.75\div100=0.0375\). On dividing by (100), the decimal point moves two places to the left.
Step 3
Exam Tip
\(x=3.75\div100=0.0375\) है। (100) से भाग देने पर दशमलव बिंदु दो स्थान बाईं ओर जाता है।
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यदि (1000x=64.8), तो (x) का मान क्या होगा?
If (1000x=64.8), what will be the value of (x)?
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A (0.648)
B (0.0648)
C (64800)
D (6.48)
Explanation opens after your attempt
Correct Answer
B. (0.0648)
Step 1
Concept
\(x=64.8\div1000=0.0648\). On dividing by (1000), the decimal point moves three places to the left.
Step 2
Why this answer is correct
The correct answer is B. (0.0648). \(x=64.8\div1000=0.0648\). On dividing by (1000), the decimal point moves three places to the left.
Step 3
Exam Tip
\(x=64.8\div1000=0.0648\) है। (1000) से भाग देने पर दशमलव बिंदु तीन स्थान बाईं ओर जाता है।
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दशमलव \(0.333\ldots\) और \( \frac{1}{3} \) के बारे में सही कथन कौन-सा है?
Which statement about \(0.333\ldots\) and \( \frac{1}{3} \) is correct?
#number-systems
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A \(0.333\ldots<\frac{1}{3}\)
B \(0.333\ldots>\frac{1}{3}\)
C \(0.333\ldots=\frac{1}{3}\)
D तुलना नहीं हो सकती / Cannot be compared
Explanation opens after your attempt
Correct Answer
C. \(0.333\ldots=\frac{1}{3}\)
Step 1
Concept
\( \frac{1}{3}=0.333\ldots \). A recurring decimal can also be written using bar notation.
Step 2
Why this answer is correct
The correct answer is C. \(0.333\ldots=\frac{1}{3}\). \( \frac{1}{3}=0.333\ldots \). A recurring decimal can also be written using bar notation.
Step 3
Exam Tip
\( \frac{1}{3}=0.333\ldots \) होता है। आवर्ती दशमलव को बार संकेतन से भी लिखा जा सकता है।
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(0.09), \( \frac{1}{11} \), (0.091) में सबसे बड़ी संख्या कौन-सी है?
Among (0.09), \( \frac{1}{11} \), and (0.091), which is the greatest number?
#number-systems
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A (0.09)
B \( \frac{1}{11} \)
C (0.091)
D तीनों बराबर हैं / All three are equal
Explanation opens after your attempt
Correct Answer
C. (0.091)
Step 1
Concept
\( \frac{1}{11}=0.0909\ldots \), which is slightly less than (0.091). Convert the fraction into decimal for comparison.
Step 2
Why this answer is correct
The correct answer is C. (0.091). \( \frac{1}{11}=0.0909\ldots \), which is slightly less than (0.091). Convert the fraction into decimal for comparison.
Step 3
Exam Tip
\( \frac{1}{11}=0.0909\ldots \), जो (0.091) से थोड़ा छोटा है। भिन्न को दशमलव में बदलकर तुलना करें।
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भिन्न \( \frac{45}{72} \) का सरल रूप लेकर दशमलव प्रसार कैसा होगा?
After simplifying \( \frac{45}{72} \), what type of decimal expansion will it 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 पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
A. सांत / Terminating
Step 1
Concept
\( \frac{45}{72}=\frac{5}{8} \) and \(8=2^3\). Therefore, its decimal expansion will be terminating.
Step 2
Why this answer is correct
The correct answer is A. सांत / Terminating. \( \frac{45}{72}=\frac{5}{8} \) and \(8=2^3\). Therefore, its decimal expansion will be terminating.
Step 3
Exam Tip
\( \frac{45}{72}=\frac{5}{8} \) और \(8=2^3\) है। इसलिए इसका दशमलव प्रसार सांत होगा।
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भिन्न \( \frac{28}{98} \) का सरल रूप लेकर दशमलव प्रसार कैसा होगा?
After simplifying \( \frac{28}{98} \), what type of decimal expansion will it have?
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A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D केवल शून्य / Only zero
Explanation opens after your attempt
Correct Answer
B. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
\( \frac{28}{98}=\frac{2}{7} \). Since the denominator has (7), the decimal will be non-terminating recurring.
Step 2
Why this answer is correct
The correct answer is B. असांत आवर्ती / Non-terminating recurring. \( \frac{28}{98}=\frac{2}{7} \). Since the denominator has (7), the decimal will be non-terminating recurring.
Step 3
Exam Tip
\( \frac{28}{98}=\frac{2}{7} \) है। हर में (7) होने से दशमलव असांत आवर्ती होगा।
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(0.0045) और (0.00045) में (0.0045) कितने गुना है?
How many times is (0.0045) of (0.00045)?
#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
\(0.0045\div0.00045=10\). 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. \(0.0045\div0.00045=10\). The difference in decimal places shows the multiplication relation.
Step 3
Exam Tip
\(0.0045\div0.00045=10\) है। दशमलव स्थानों का अंतर गुणन संबंध बताता है।
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(0.125) को (0.001) से भाग देने पर क्या मिलेगा?
What is obtained by dividing (0.125) by (0.001)?
#number-systems
#decimal-representation
#decimal-division
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A (1.25)
B (12.5)
C (125)
D (0.125)
Explanation opens after your attempt
Step 1
Concept
\(0.125\div0.001=125\). Dividing by (0.001) is like multiplying by (1000).
Step 2
Why this answer is correct
The correct answer is C. (125). \(0.125\div0.001=125\). Dividing by (0.001) is like multiplying by (1000).
Step 3
Exam Tip
\(0.125\div0.001=125\) है। (0.001) से भाग देना (1000) से गुणा करने जैसा है।
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दशमलव \(0.120120012000120000\ldots\) किस प्रकार का है?
What type of decimal is \(0.120120012000120000\ldots\)?
#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 परिमेय पूर्णांक / Rational integer
Explanation opens after your attempt
Correct Answer
C. असांत अनावर्ती / Non-terminating non-recurring
Step 1
Concept
It has no fixed repeating block and it does not terminate. 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. It has no fixed repeating block and it does not terminate. Such a decimal is non-terminating non-recurring.
Step 3
Exam Tip
इसमें कोई निश्चित दोहराने वाला समूह नहीं है और यह समाप्त नहीं होता। ऐसा दशमलव असांत अनावर्ती होता है।
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कौन-सा दशमलव \( \frac{2}{5} \) से बड़ा और \( \frac{1}{2} \) से छोटा है?
Which decimal is greater than \( \frac{2}{5} \) and less than \( \frac{1}{2} \)?
#number-systems
#decimal-representation
#between-decimals
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A (0.39)
B (0.405)
C (0.500)
D (0.52)
Explanation opens after your attempt
Correct Answer
B. (0.405)
Step 1
Concept
\( \frac{2}{5}=0.4 \) and \( \frac{1}{2}=0.5 \), so (0.405) lies between them. Convert the boundaries into decimals.
Step 2
Why this answer is correct
The correct answer is B. (0.405). \( \frac{2}{5}=0.4 \) and \( \frac{1}{2}=0.5 \), so (0.405) lies between them. Convert the boundaries into decimals.
Step 3
Exam Tip
\( \frac{2}{5}=0.4 \) और \( \frac{1}{2}=0.5 \), इसलिए (0.405) इनके बीच है। सीमाओं को दशमलव में बदलें।
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(3.006), (3.060), (3.600), (3.066) का घटता क्रम कौन-सा है?
What is the descending order of (3.006), (3.060), (3.600), and (3.066)?
#number-systems
#decimal-representation
#descending-order
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A (3.600>3.066>3.060>3.006)
B (3.066>3.600>3.060>3.006)
C (3.006>3.060>3.066>3.600)
D (3.600>3.006>3.060>3.066)
Explanation opens after your attempt
Correct Answer
A. (3.600>3.066>3.060>3.006)
Step 1
Concept
(3.600) is greatest at the tenths place and (3.006) is smallest. In descending order, write from greatest to smallest.
Step 2
Why this answer is correct
The correct answer is A. (3.600>3.066>3.060>3.006). (3.600) is greatest at the tenths place and (3.006) is smallest. In descending order, write from greatest to smallest.
Step 3
Exam Tip
दसवें स्थान पर (3.600) सबसे बड़ा है और (3.006) सबसे छोटा है। घटते क्रम में बड़े से छोटे की ओर लिखें।
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भिन्न \( \frac{53}{800} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{53}{800} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.06625)
B (0.6625)
C (0.0538)
D (0.006625)
Explanation opens after your attempt
Correct Answer
A. (0.06625)
Step 1
Concept
\(800\times125=100000\), so \( \frac{53}{800}=\frac{6625}{100000}=0.06625 \). Convert the denominator into a power of (10) to find the decimal.
Step 2
Why this answer is correct
The correct answer is A. (0.06625). \(800\times125=100000\), so \( \frac{53}{800}=\frac{6625}{100000}=0.06625 \). Convert the denominator into a power of (10) to find the decimal.
Step 3
Exam Tip
\(800\times125=100000\), इसलिए \( \frac{53}{800}=\frac{6625}{100000}=0.06625 \) है। हर को (10) की घात बनाकर दशमलव निकालें।
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दशमलव (0.00375) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.00375) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{3}{800} \)
B \( \frac{375}{10000} \)
C \( \frac{15}{400} \)
D \( \frac{1}{375} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{3}{800} \)
Step 1
Concept
\(0.00375=\frac{375}{100000}=\frac{3}{800}\). For five decimal places, use denominator (100000) and simplify the fraction.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{3}{800} \). \(0.00375=\frac{375}{100000}=\frac{3}{800}\). For five decimal places, use denominator (100000) and simplify the fraction.
Step 3
Exam Tip
\(0.00375=\frac{375}{100000}=\frac{3}{800}\) है। पांच दशमलव स्थान हों तो हर (100000) लें और भिन्न सरल करें।
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यदि (0.72b<0.728), तो अंक (b) का सबसे बड़ा मान क्या हो सकता है?
If (0.72b<0.728), what can be the greatest value of digit (b)?
#number-systems
#decimal-representation
#decimal-comparison
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The tenths and hundredths digits are equal, so the thousandths digit must satisfy (b<8). Hence the greatest 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 (b<8). Hence the greatest value is (7).
Step 3
Exam Tip
दसवें और सौवें स्थान समान हैं, इसलिए हजारवें स्थान पर (b<8) होना चाहिए। अतः सबसे बड़ा मान (7) है।
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दशमलव \(6.020202\ldots\) का आवर्ती भाग क्या है?
What is the recurring part of \(6.020202\ldots\)?
#number-systems
#decimal-representation
#repeating-block
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A (6)
B (02)
C (20)
D (202)
Explanation opens after your attempt
Step 1
Concept
In the decimal part, the block (02) repeats again and again. Identify the recurring part in the same order.
Step 2
Why this answer is correct
The correct answer is B. (02). In the decimal part, the block (02) repeats again and again. Identify the recurring part in the same order.
Step 3
Exam Tip
दशमलव भाग में (02) का समूह बार-बार दोहरता है। आवर्ती भाग को उसी क्रम में पहचानें।
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