भिन्न \( \frac{23}{125} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{23}{125} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.184)
B (0.23)
C (1.84)
D (0.125)
Explanation opens after your attempt
Correct Answer
A. (0.184)
Step 1
Concept
\(125\times8=1000\), so \( \frac{23}{125}=\frac{184}{1000}=0.184 \). Making the denominator a power of (10) is a fast method.
Step 2
Why this answer is correct
The correct answer is A. (0.184). \(125\times8=1000\), so \( \frac{23}{125}=\frac{184}{1000}=0.184 \). Making the denominator a power of (10) is a fast method.
Step 3
Exam Tip
\(125\times8=1000\), इसलिए \( \frac{23}{125}=\frac{184}{1000}=0.184 \) है। हर को (10) की घात बनाना तेज तरीका है।
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दशमलव (0.5625) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.5625) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{9}{16} \)
B \( \frac{56}{25} \)
C \( \frac{45}{80} \)
D \( \frac{5625}{1000} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{9}{16} \)
Step 1
Concept
\(0.5625=\frac{5625}{10000}=\frac{9}{16}\). First write the decimal as a fraction and then simplify.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{9}{16} \). \(0.5625=\frac{5625}{10000}=\frac{9}{16}\). First write the decimal as a fraction and then simplify.
Step 3
Exam Tip
\(0.5625=\frac{5625}{10000}=\frac{9}{16}\) है। दशमलव को पहले भिन्न में लिखें और फिर सरल करें।
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सरल रूप में \( \frac{17}{120} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{17}{120} \) 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 पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
B. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
\(120=2^3\times3\times5\) also has (3). So this rational number gives a non-terminating recurring decimal.
Step 2
Why this answer is correct
The correct answer is B. असांत आवर्ती / Non-terminating recurring. \(120=2^3\times3\times5\) also has (3). So this rational number gives a non-terminating recurring decimal.
Step 3
Exam Tip
\(120=2^3\times3\times5\) में (3) भी है। इसलिए यह परिमेय संख्या असांत आवर्ती दशमलव देगी।
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दशमलव (4.0705) में (7) का स्थानीय मान क्या है?
What is the place value of (7) in (4.0705)?
#number-systems
#decimal-representation
#place-value
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A \( \frac{7}{10} \)
B \( \frac{7}{100} \)
C \( \frac{7}{1000} \)
D (7)
Explanation opens after your attempt
Correct Answer
B. \( \frac{7}{100} \)
Step 1
Concept
(7) 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. \( \frac{7}{100} \). (7) is in the second place after the decimal point. The second decimal place is hundredths.
Step 3
Exam Tip
(7) दशमलव के बाद दूसरे स्थान पर है। दूसरा दशमलव स्थान सौवां होता है।
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दशमलव (3.208) का विस्तारित रूप कौन-सा है?
Which is the expanded form of (3.208)?
#number-systems
#decimal-representation
#expanded-form
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A \(3+\frac{2}{10}+\frac{8}{100}\)
B \(3+\frac{2}{100}+\frac{8}{1000}\)
C \(3+\frac{2}{10}+\frac{8}{1000}\)
D \(32+\frac{8}{1000}\)
Explanation opens after your attempt
Correct Answer
C. \(3+\frac{2}{10}+\frac{8}{1000}\)
Step 1
Concept
(2) is in tenths and (8) is in thousandths. The middle (0) shows the hundredths place.
Step 2
Why this answer is correct
The correct answer is C. \(3+\frac{2}{10}+\frac{8}{1000}\). (2) is in tenths and (8) is in thousandths. The middle (0) shows the hundredths place.
Step 3
Exam Tip
(2) दसवें और (8) हजारवें स्थान पर है। बीच का (0) सौवें स्थान को दिखाता है।
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दशमलव \(0.1454545\ldots\) में आवर्ती भाग कौन-सा है?
What is the recurring part in \(0.1454545\ldots\)?
#number-systems
#decimal-representation
#repeating-block
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A (14)
B (45)
C (54)
D (145)
Explanation opens after your attempt
Step 1
Concept
After the first (1), the block (45) repeats continuously. The recurring part is the smallest repeating block.
Step 2
Why this answer is correct
The correct answer is B. (45). After the first (1), the block (45) repeats continuously. The recurring part is the smallest repeating block.
Step 3
Exam Tip
पहले (1) के बाद (45) का समूह लगातार दोहरता है। आवर्ती भाग सबसे छोटा दोहराने वाला समूह होता है।
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भिन्न \( \frac{7}{12} \) का दशमलव प्रसार कौन-सा है?
Which is the decimal expansion of \( \frac{7}{12} \)?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.58333\ldots\)
B \(0.71212\ldots\)
C (0.75)
D \(0.5714\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(0.58333\ldots\)
Step 1
Concept
\(7\div12=0.58333\ldots\). While dividing, identify the repeating digit.
Step 2
Why this answer is correct
The correct answer is A. \(0.58333\ldots\). \(7\div12=0.58333\ldots\). While dividing, identify the repeating digit.
Step 3
Exam Tip
\(7\div12=0.58333\ldots\) होता है। भाग देते समय दोहराने वाले अंक को पहचानें।
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कौन-सी संख्या (1.04) और (1.05) के बीच है?
Which number lies between (1.04) and (1.05)?
#number-systems
#decimal-representation
#between-decimals
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A (1.039)
B (1.050)
C (1.045)
D (1.055)
Explanation opens after your attempt
Correct Answer
C. (1.045)
Step 1
Concept
(1.045) is greater than (1.040) and less than (1.050). Make decimal places equal to find a number between them.
Step 2
Why this answer is correct
The correct answer is C. (1.045). (1.045) is greater than (1.040) and less than (1.050). Make decimal places equal to find a number between them.
Step 3
Exam Tip
(1.045), (1.040) से बड़ा और (1.050) से छोटा है। बीच की संख्या खोजने के लिए दशमलव स्थान समान करें।
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दशमलव (0.07007) में पहले (7) का स्थानीय मान क्या है?
What is the place value of the first (7) in (0.07007)?
#number-systems
#decimal-representation
#place-value
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A \( \frac{7}{10} \)
B \( \frac{7}{100} \)
C \( \frac{7}{1000} \)
D \( \frac{7}{10000} \)
Explanation opens after your attempt
Correct Answer
B. \( \frac{7}{100} \)
Step 1
Concept
The first (7) is in the second place after the decimal point. So its place value is \( \frac{7}{100} \).
Step 2
Why this answer is correct
The correct answer is B. \( \frac{7}{100} \). The first (7) is in the second place after the decimal point. So its place value is \( \frac{7}{100} \).
Step 3
Exam Tip
पहला (7) दशमलव के बाद दूसरे स्थान पर है। इसलिए उसका स्थानीय मान \( \frac{7}{100} \) है।
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(6.25) को अनुचित भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (6.25) is converted into an improper fraction?
#number-systems
#decimal-representation
#improper-fraction
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A \( \frac{25}{4} \)
B \( \frac{625}{10} \)
C \( \frac{6}{25} \)
D \( \frac{31}{5} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{25}{4} \)
Step 1
Concept
\(6.25=\frac{625}{100}=\frac{25}{4}\). Convert the decimal to a fraction and simplify the final answer.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{25}{4} \). \(6.25=\frac{625}{100}=\frac{25}{4}\). Convert the decimal to a fraction and simplify the final answer.
Step 3
Exam Tip
\(6.25=\frac{625}{100}=\frac{25}{4}\) है। दशमलव को भिन्न में बदलकर अंतिम उत्तर सरल करें।
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दशमलव (0.00625) को सरल भिन्न में लिखने पर क्या मिलेगा?
What is obtained when (0.00625) is written as a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{1}{160} \)
B \( \frac{1}{16} \)
C \( \frac{625}{1000} \)
D \( \frac{1}{625} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{1}{160} \)
Step 1
Concept
\(0.00625=\frac{625}{100000}=\frac{1}{160}\). For five decimal places, use denominator (100000).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{1}{160} \). \(0.00625=\frac{625}{100000}=\frac{1}{160}\). For five decimal places, use denominator (100000).
Step 3
Exam Tip
\(0.00625=\frac{625}{100000}=\frac{1}{160}\) है। पांच दशमलव स्थान हों तो हर (100000) लें।
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कौन-सा दशमलव (0.3040) के बराबर नहीं है?
Which decimal is not equal to (0.3040)?
#number-systems
#decimal-representation
#equivalent-decimals
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A (0.304)
B (0.30400)
C (0.0304)
D (0.304000)
Explanation opens after your attempt
Correct Answer
C. (0.0304)
Step 1
Concept
In (0.0304), the place of digits has changed, so it is smaller. Only adding or removing zeros at the end does not change value.
Step 2
Why this answer is correct
The correct answer is C. (0.0304). In (0.0304), the place of digits has changed, so it is smaller. Only adding or removing zeros at the end does not change value.
Step 3
Exam Tip
(0.0304) में अंकों का स्थान बदल गया है, इसलिए यह छोटा है। केवल अंत में शून्य जोड़ने या हटाने से मान नहीं बदलता।
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(0.064) को प्रतिशत में बदलने पर क्या मिलेगा?
What is obtained by converting (0.064) into a percentage?
#number-systems
#decimal-representation
#decimal-percent
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A (64%)
B (6.4%)
C (0.64%)
D (0.064%)
Explanation opens after your attempt
Step 1
Concept
\(0.064\times100=6.4\), so it becomes (6.4%). To convert a decimal into a percentage, multiply by (100).
Step 2
Why this answer is correct
The correct answer is B. (6.4%). \(0.064\times100=6.4\), so it becomes (6.4%). To convert a decimal into a percentage, multiply by (100).
Step 3
Exam Tip
\(0.064\times100=6.4\), इसलिए (6.4%) मिलेगा। दशमलव को प्रतिशत में बदलने के लिए (100) से गुणा करें।
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(8.406) को (100) से भाग देने पर क्या मिलेगा?
What is obtained by dividing (8.406) by (100)?
#number-systems
#decimal-representation
#decimal-division
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A (840.6)
B (0.8406)
C (0.08406)
D (0.008406)
Explanation opens after your attempt
Correct Answer
C. (0.08406)
Step 1
Concept
\(8.406\div100=0.08406\). 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. (0.08406). \(8.406\div100=0.08406\). On dividing by (100), the decimal point moves two places to the left.
Step 3
Exam Tip
\(8.406\div100=0.08406\) होता है। (100) से भाग देने पर दशमलव बिंदु दो स्थान बाईं ओर जाता है।
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(0.375+0.0625) का मान क्या है?
What is the value of (0.375+0.0625)?
#number-systems
#decimal-representation
#decimal-addition
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A (0.4375)
B (0.3875)
C (0.3125)
D (0.6250)
Explanation opens after your attempt
Correct Answer
A. (0.4375)
Step 1
Concept
(0.3750+0.0625=0.4375). Align decimal points while adding.
Step 2
Why this answer is correct
The correct answer is A. (0.4375). (0.3750+0.0625=0.4375). Align decimal points while adding.
Step 3
Exam Tip
(0.3750+0.0625=0.4375) है। जोड़ते समय दशमलव बिंदुओं को एक सीध में रखें।
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(5.5-2.875) का मान क्या है?
What is the value of (5.5-2.875)?
#number-systems
#decimal-representation
#decimal-subtraction
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A (2.725)
B (2.625)
C (3.125)
D (2.875)
Explanation opens after your attempt
Correct Answer
B. (2.625)
Step 1
Concept
(5.5=5.500), so (5.500-2.875=2.625). Add zeros in empty decimal places while subtracting.
Step 2
Why this answer is correct
The correct answer is B. (2.625). (5.5=5.500), so (5.500-2.875=2.625). Add zeros in empty decimal places while subtracting.
Step 3
Exam Tip
(5.5=5.500), इसलिए (5.500-2.875=2.625) है। घटाते समय खाली दशमलव स्थानों में शून्य लगाएं।
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दशमलव \(3.14114111411114\ldots\) कैसा है?
What type of decimal is \(3.14114111411114\ldots\)?
#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 पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
C. असांत अनावर्ती / Non-terminating non-recurring
Step 1
Concept
It has no fixed repeating part 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 part and it does not terminate. Such a decimal is non-terminating non-recurring.
Step 3
Exam Tip
इसमें निश्चित दोहराने वाला भाग नहीं है और यह समाप्त भी नहीं होता। ऐसा दशमलव असांत अनावर्ती होता है।
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भिन्न \( \frac{5}{22} \) का दशमलव प्रसार कौन-सा है?
Which is the decimal expansion of \( \frac{5}{22} \)?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.2272727\ldots\)
B \(0.52222\ldots\)
C \(0.252525\ldots\)
D (0.22)
Explanation opens after your attempt
Correct Answer
A. \(0.2272727\ldots\)
Step 1
Concept
\(5\div22=0.2272727\ldots\). Here the block (27) repeats.
Step 2
Why this answer is correct
The correct answer is A. \(0.2272727\ldots\). \(5\div22=0.2272727\ldots\). Here the block (27) repeats.
Step 3
Exam Tip
\(5\div22=0.2272727\ldots\) होता है। यहां (27) का समूह दोहरता है।
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सरल रूप में \( \frac{63}{84} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{63}{84} \) have?
#number-systems
#decimal-representation
#simplest-form-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
\( \frac{63}{84}=\frac{3}{4} \) and \(4=2^2\). Therefore, its decimal expansion will be terminating.
Step 2
Why this answer is correct
The correct answer is C. सांत / Terminating. \( \frac{63}{84}=\frac{3}{4} \) and \(4=2^2\). Therefore, its decimal expansion will be terminating.
Step 3
Exam Tip
\( \frac{63}{84}=\frac{3}{4} \) और \(4=2^2\) है। इसलिए इसका दशमलव प्रसार सांत होगा।
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सरल रूप में \( \frac{44}{66} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{44}{66} \) 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
\( \frac{44}{66}=\frac{2}{3} \). 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. \( \frac{44}{66}=\frac{2}{3} \). Since the denominator has (3), the decimal will be non-terminating recurring.
Step 3
Exam Tip
\( \frac{44}{66}=\frac{2}{3} \) है। हर में (3) होने के कारण दशमलव असांत आवर्ती होगा।
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दशमलव \(0.036036036\ldots\) का सही बार संकेतन कौन-सा है?
Which is the correct bar notation of \(0.036036036\ldots\)?
#number-systems
#decimal-representation
#bar-notation
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A \(0.\overline{36}\)
B \(0.0\overline{36}\)
C \(0.\overline{036}\)
D \(0.03\overline{6}\)
Explanation opens after your attempt
Correct Answer
C. \(0.\overline{036}\)
Step 1
Concept
The whole block (036) is repeating. The bar should be placed over the entire recurring part.
Step 2
Why this answer is correct
The correct answer is C. \(0.\overline{036}\). The whole block (036) is repeating. The bar should be placed over the entire recurring part.
Step 3
Exam Tip
(036) का पूरा समूह बार-बार आ रहा है। बार पूरे आवर्ती भाग पर लगाना चाहिए।
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\(0.0909\ldots\) और (0.09) के बारे में सही कथन कौन-सा है?
Which statement about \(0.0909\ldots\) and (0.09) is correct?
#number-systems
#decimal-representation
#compare-decimals
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A \(0.0909\ldots<0.09\)
B \(0.0909\ldots=0.09\)
C \(0.0909\ldots>0.09\)
D तुलना नहीं हो सकती / Cannot be compared
Explanation opens after your attempt
Correct Answer
C. \(0.0909\ldots>0.09\)
Step 1
Concept
\(0.0909\ldots\) is greater than \(0.0900\ldots\). Think of both in comparable decimal form.
Step 2
Why this answer is correct
The correct answer is C. \(0.0909\ldots>0.09\). \(0.0909\ldots\) is greater than \(0.0900\ldots\). Think of both in comparable decimal form.
Step 3
Exam Tip
\(0.0909\ldots\), \(0.0900\ldots\) से बड़ा है। तुलना में दोनों को समान दशमलव रूप में सोचें।
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यदि (1000x=7.25), तो (x) का मान क्या है?
If (1000x=7.25), what is the value of (x)?
#number-systems
#decimal-representation
#decimal-division
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A (7250)
B (0.725)
C (0.0725)
D (0.00725)
Explanation opens after your attempt
Correct Answer
D. (0.00725)
Step 1
Concept
\(x=7.25\div1000=0.00725\). On dividing by (1000), the decimal point moves three places to the left.
Step 2
Why this answer is correct
The correct answer is D. (0.00725). \(x=7.25\div1000=0.00725\). On dividing by (1000), the decimal point moves three places to the left.
Step 3
Exam Tip
\(x=7.25\div1000=0.00725\) है। (1000) से भाग देने पर दशमलव बिंदु तीन स्थान बाईं ओर जाता है।
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दशमलव (0.875) को मिश्रित प्रतिशत के रूप में क्या लिखेंगे?
How is (0.875) written as a percentage?
#number-systems
#decimal-representation
#decimal-percent
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A (8.75%)
B (87.5%)
C (875%)
D (0.875%)
Explanation opens after your attempt
Correct Answer
B. (87.5%)
Step 1
Concept
\(0.875\times100=87.5\), so it is (87.5%). Multiply by (100) to convert into percentage.
Step 2
Why this answer is correct
The correct answer is B. (87.5%). \(0.875\times100=87.5\), so it is (87.5%). Multiply by (100) to convert into percentage.
Step 3
Exam Tip
\(0.875\times100=87.5\), इसलिए (87.5%) है। प्रतिशत में बदलने के लिए (100) से गुणा करें।
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कौन-सा दशमलव \( \frac{11}{16} \) के बराबर है?
Which decimal is equal to \( \frac{11}{16} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.1116)
B (0.625)
C (0.6875)
D (0.716)
Explanation opens after your attempt
Correct Answer
C. (0.6875)
Step 1
Concept
\(16\times625=10000\), so \( \frac{11}{16}=\frac{6875}{10000}=0.6875 \). Convert the denominator into a power of (10).
Step 2
Why this answer is correct
The correct answer is C. (0.6875). \(16\times625=10000\), so \( \frac{11}{16}=\frac{6875}{10000}=0.6875 \). Convert the denominator into a power of (10).
Step 3
Exam Tip
\(16\times625=10000\), इसलिए \( \frac{11}{16}=\frac{6875}{10000}=0.6875 \) है। हर को (10) की घात में बदलें।
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दशमलव (12.3045) में (5) का स्थानीय मान क्या है?
What is the place value of (5) in (12.3045)?
#number-systems
#decimal-representation
#place-value
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A \( \frac{5}{10} \)
B \( \frac{5}{100} \)
C \( \frac{5}{1000} \)
D \( \frac{5}{10000} \)
Explanation opens after your attempt
Correct Answer
D. \( \frac{5}{10000} \)
Step 1
Concept
(5) 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 D. \( \frac{5}{10000} \). (5) is in the fourth place after the decimal point. The fourth decimal place is ten-thousandths.
Step 3
Exam Tip
(5) दशमलव के बाद चौथे स्थान पर है। चौथा दशमलव स्थान दस हजारवां होता है।
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किस विकल्प में सभी संख्याएं असांत आवर्ती हैं?
In which option are all numbers non-terminating recurring?
#number-systems
#decimal-representation
#recurring-decimal
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A \(0.\overline{6}\), \(1.2323\ldots\), \(4.105105\ldots\)
B (0.25), \(0.\overline{7}\), (2.5)
C \(3.14159\ldots\), (0.5), \(1.333\ldots\)
D (6.125), (7.04), (8.9)
Explanation opens after your attempt
Correct Answer
A. \(0.\overline{6}\), \(1.2323\ldots\), \(4.105105\ldots\)
Step 1
Concept
All numbers in the first option have some part repeating again and again. This is the key feature of non-terminating recurring decimals.
Step 2
Why this answer is correct
The correct answer is A. \(0.\overline{6}\), \(1.2323\ldots\), \(4.105105\ldots\). All numbers in the first option have some part repeating again and again. This is the key feature of non-terminating recurring decimals.
Step 3
Exam Tip
पहले विकल्प की सभी संख्याओं में कोई न कोई भाग बार-बार दोहरता है। यही असांत आवर्ती दशमलव की पहचान है।
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दशमलव (0.0048) को सरल भिन्न में बदलने पर क्या मिलेगा?
What is obtained when (0.0048) is converted into a simplified fraction?
#number-systems
#decimal-representation
#decimal-to-fraction
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A \( \frac{3}{625} \)
B \( \frac{48}{1000} \)
C \( \frac{12}{250} \)
D \( \frac{4}{800} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{3}{625} \)
Step 1
Concept
\(0.0048=\frac{48}{10000}=\frac{3}{625}\). Count decimal places to write the correct denominator.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{3}{625} \). \(0.0048=\frac{48}{10000}=\frac{3}{625}\). Count decimal places to write the correct denominator.
Step 3
Exam Tip
\(0.0048=\frac{48}{10000}=\frac{3}{625}\) है। दशमलव स्थान गिनकर सही हर लिखें।
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(0.2), (0.0202), (0.022), (0.202) को बढ़ते क्रम में कौन-सा सही है?
Which is the correct ascending order of (0.2), (0.0202), (0.022), and (0.202)?
#number-systems
#decimal-representation
#ascending-order
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A (0.0202<0.022<0.2<0.202)
B (0.2<0.202<0.022<0.0202)
C (0.022<0.0202<0.2<0.202)
D (0.202<0.2<0.022<0.0202)
Explanation opens after your attempt
Correct Answer
A. (0.0202<0.022<0.2<0.202)
Step 1
Concept
(0.0202) is the smallest and (0.202) is the greatest. Write all numbers up to equal decimal places for comparison.
Step 2
Why this answer is correct
The correct answer is A. (0.0202<0.022<0.2<0.202). (0.0202) is the smallest and (0.202) is the greatest. Write all numbers up to equal decimal places for comparison.
Step 3
Exam Tip
(0.0202) सबसे छोटा और (0.202) सबसे बड़ा है। तुलना के लिए सभी को समान दशमलव स्थान तक लिखें।
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दशमलव (5.6006) का विस्तारित रूप कौन-सा है?
Which is the expanded form of (5.6006)?
#number-systems
#decimal-representation
#expanded-form
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A \(5+\frac{6}{10}+\frac{6}{10000}\)
B \(5+\frac{6}{100}+\frac{6}{1000}\)
C \(5+\frac{60}{100}+\frac{6}{100}\)
D \(56+\frac{6}{10000}\)
Explanation opens after your attempt
Correct Answer
A. \(5+\frac{6}{10}+\frac{6}{10000}\)
Step 1
Concept
The first (6) is in tenths and the last (6) is in ten-thousandths. So the expanded form is \(5+\frac{6}{10}+\frac{6}{10000}\).
Step 2
Why this answer is correct
The correct answer is A. \(5+\frac{6}{10}+\frac{6}{10000}\). The first (6) is in tenths and the last (6) is in ten-thousandths. So the expanded form is \(5+\frac{6}{10}+\frac{6}{10000}\).
Step 3
Exam Tip
पहला (6) दसवें और अंतिम (6) दस हजारवें स्थान पर है। इसलिए विस्तारित रूप \(5+\frac{6}{10}+\frac{6}{10000}\) है।
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भिन्न \( \frac{13}{40} \) और दशमलव (0.32) में कौन बड़ा है?
Which is greater between \( \frac{13}{40} \) and (0.32)?
#number-systems
#decimal-representation
#compare-fraction-decimal
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A \( \frac{13}{40} \)
B (0.32)
C दोनों बराबर हैं / Both are equal
D तुलना नहीं हो सकती / Cannot be compared
Explanation opens after your attempt
Correct Answer
A. \( \frac{13}{40} \)
Step 1
Concept
\( \frac{13}{40}=0.325 \), which is greater than (0.32). Convert the fraction into a decimal to compare.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{13}{40} \). \( \frac{13}{40}=0.325 \), which is greater than (0.32). Convert the fraction into a decimal to compare.
Step 3
Exam Tip
\( \frac{13}{40}=0.325 \), जो (0.32) से बड़ा है। भिन्न को दशमलव में बदलकर तुलना करें।
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यदि \( \frac{p}{q} \) सरल रूप में है और \(q=2^4\times5^3\), तो दशमलव प्रसार कैसा होगा?
If \( \frac{p}{q} \) is in simplest form and \(q=2^4\times5^3\), 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 \(q=3^2\times5\), तो दशमलव प्रसार कैसा होगा?
If \( \frac{p}{q} \) is in simplest form and \(q=3^2\times5\), 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 पूर्णांक / Always integer
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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(0.007) और (0.0007) में (0.007) कितने गुना है?
How many times is (0.007) of (0.0007)?
#number-systems
#decimal-representation
#decimal-comparison
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A (1) गुना / (1) time
B (7) गुना / (7) times
C (10) गुना / (10) times
D (100) गुना / (100) times
Explanation opens after your attempt
Correct Answer
C. (10) गुना / (10) times
Step 1
Concept
\(0.007\div0.0007=10\). The difference in decimal places shows the multiplication relation.
Step 2
Why this answer is correct
The correct answer is C. (10) गुना / (10) times. \(0.007\div0.0007=10\). The difference in decimal places shows the multiplication relation.
Step 3
Exam Tip
\(0.007\div0.0007=10\) है। दशमलव स्थानों का अंतर गुणन संबंध दिखाता है।
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दशमलव \(2.909090\ldots\) का आवर्ती भाग क्या है?
What is the recurring part of \(2.909090\ldots\)?
#number-systems
#decimal-representation
#repeating-block
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A (9)
B (90)
C (09)
D (290)
Explanation opens after your attempt
Step 1
Concept
In the decimal part, the block (90) repeats again and again. Therefore, the recurring part is (90).
Step 2
Why this answer is correct
The correct answer is B. (90). In the decimal part, the block (90) repeats again and again. Therefore, the recurring part is (90).
Step 3
Exam Tip
दशमलव भाग में (90) का समूह बार-बार दोहरता है। इसलिए आवर्ती भाग (90) है।
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(0.875), (0.857), (0.8705), (0.87) में सबसे बड़ी संख्या कौन-सी है?
Among (0.875), (0.857), (0.8705), and (0.87), which is the greatest number?
#number-systems
#decimal-representation
#compare-decimals
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A (0.875)
B (0.857)
C (0.8705)
D (0.87)
Explanation opens after your attempt
Correct Answer
A. (0.875)
Step 1
Concept
(0.8750) is greater than (0.8705), (0.8700), and (0.8570). Write equal decimal places for comparison.
Step 2
Why this answer is correct
The correct answer is A. (0.875). (0.8750) is greater than (0.8705), (0.8700), and (0.8570). Write equal decimal places for comparison.
Step 3
Exam Tip
(0.8750), (0.8705), (0.8700) और (0.8570) से बड़ा है। तुलना में समान दशमलव स्थान लिखें।
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कौन-सा दशमलव \( \frac{1}{3} \) से बड़ा और \( \frac{1}{2} \) से छोटा है?
Which decimal is greater than \( \frac{1}{3} \) and less than \( \frac{1}{2} \)?
#number-systems
#decimal-representation
#between-decimals
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A (0.25)
B (0.34)
C (0.50)
D (0.6)
Explanation opens after your attempt
Step 1
Concept
\( \frac{1}{3}=0.333\ldots \) and \( \frac{1}{2}=0.5 \), so (0.34) lies between them. Convert boundaries to decimals for comparison.
Step 2
Why this answer is correct
The correct answer is B. (0.34). \( \frac{1}{3}=0.333\ldots \) and \( \frac{1}{2}=0.5 \), so (0.34) lies between them. Convert boundaries to decimals for comparison.
Step 3
Exam Tip
\( \frac{1}{3}=0.333\ldots \) और \( \frac{1}{2}=0.5 \), इसलिए (0.34) बीच में है। सीमाओं को दशमलव में बदलकर तुलना करें।
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भिन्न \( \frac{41}{200} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{41}{200} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.0205)
B (0.205)
C (0.41)
D (2.05)
Explanation opens after your attempt
Correct Answer
B. (0.205)
Step 1
Concept
\( \frac{41}{200}=\frac{205}{1000}=0.205 \). Multiply denominator (200) by (5) to make (1000).
Step 2
Why this answer is correct
The correct answer is B. (0.205). \( \frac{41}{200}=\frac{205}{1000}=0.205 \). Multiply denominator (200) by (5) to make (1000).
Step 3
Exam Tip
\( \frac{41}{200}=\frac{205}{1000}=0.205 \) है। हर (200) को (1000) बनाने के लिए (5) से गुणा करें।
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दशमलव (7.04004) में अंतिम (4) का स्थानीय मान क्या है?
What is the place value of the last (4) in (7.04004)?
#number-systems
#decimal-representation
#place-value
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A \( \frac{4}{10} \)
B \( \frac{4}{100} \)
C \( \frac{4}{1000} \)
D \( \frac{4}{100000} \)
Explanation opens after your attempt
Correct Answer
D. \( \frac{4}{100000} \)
Step 1
Concept
The last (4) 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 D. \( \frac{4}{100000} \). The last (4) is in the fifth place after the decimal point. The fifth decimal place is hundred-thousandths.
Step 3
Exam Tip
अंतिम (4) दशमलव के बाद पांचवें स्थान पर है। पांचवां दशमलव स्थान लाखवां होता है।
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(12.5) को (0.1) से गुणा करने पर क्या मिलेगा?
What is obtained by multiplying (12.5) by (0.1)?
#number-systems
#decimal-representation
#decimal-multiplication
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A (125)
B (12.50)
C (1.25)
D (0.125)
Explanation opens after your attempt
Step 1
Concept
\(12.5\times0.1=1.25\). Multiplying by (0.1) is like dividing by (10).
Step 2
Why this answer is correct
The correct answer is C. (1.25). \(12.5\times0.1=1.25\). Multiplying by (0.1) is like dividing by (10).
Step 3
Exam Tip
\(12.5\times0.1=1.25\) है। (0.1) से गुणा करना (10) से भाग देने जैसा है।
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\(0.36\div0.12\) का मान क्या है?
What is the value of \(0.36\div0.12\)?
#number-systems
#decimal-representation
#decimal-division
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A (0.3)
B (3)
C (30)
D (0.03)
Explanation opens after your attempt
Step 1
Concept
Multiplying both by (100) gives \(36\div12=3\). 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. (3). Multiplying both by (100) gives \(36\div12=3\). Multiplying both parts of a division by the same number does not change the quotient.
Step 3
Exam Tip
दोनों को (100) से गुणा करने पर \(36\div12=3\) मिलता है। दशमलव भाग में समान गुणा करने से भागफल नहीं बदलता।
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कौन-सा दशमलव असांत अनावर्ती हो सकता है?
Which decimal can be non-terminating non-recurring?
#number-systems
#decimal-representation
#irrational-decimal
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A \(0.454545\ldots\)
B (1.625)
C \(2.7182818\ldots\) बिना निश्चित दोहराव / \(2.7182818\ldots\) without fixed repetition
D \(5.\overline{12}\)
Explanation opens after your attempt
Correct Answer
C. \(2.7182818\ldots\) बिना निश्चित दोहराव / \(2.7182818\ldots\) without fixed repetition
Step 1
Concept
A non-terminating decimal without fixed repetition is non-terminating non-recurring. Such decimals can represent irrational numbers.
Step 2
Why this answer is correct
The correct answer is C. \(2.7182818\ldots\) बिना निश्चित दोहराव / \(2.7182818\ldots\) without fixed repetition. A non-terminating decimal without fixed repetition is non-terminating non-recurring. Such decimals can represent irrational numbers.
Step 3
Exam Tip
बिना निश्चित दोहराव वाला असांत दशमलव असांत अनावर्ती होता है। ऐसे दशमलव अपरिमेय संख्या का रूप हो सकते हैं।
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भिन्न \( \frac{14}{25} \) और (0.56) के बारे में सही कथन कौन-सा है?
Which statement about \( \frac{14}{25} \) and (0.56) is correct?
#number-systems
#decimal-representation
#compare-fraction-decimal
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A \( \frac{14}{25}<0.56 \)
B \( \frac{14}{25}>0.56 \)
C \( \frac{14}{25}=0.56 \)
D तुलना नहीं हो सकती / Cannot be compared
Explanation opens after your attempt
Correct Answer
C. \( \frac{14}{25}=0.56 \)
Step 1
Concept
\( \frac{14}{25}=\frac{56}{100}=0.56 \). Making the denominator (100) makes comparison easy.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{14}{25}=0.56 \). \( \frac{14}{25}=\frac{56}{100}=0.56 \). Making the denominator (100) makes comparison easy.
Step 3
Exam Tip
\( \frac{14}{25}=\frac{56}{100}=0.56 \) है। हर को (100) बनाकर तुलना आसान हो जाती है।
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दशमलव \(0.312312312\ldots\) को बार संकेतन में कैसे लिखेंगे?
How is \(0.312312312\ldots\) written in bar notation?
#number-systems
#decimal-representation
#bar-notation
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A \(0.\overline{31}\)
B \(0.3\overline{12}\)
C \(0.\overline{312}\)
D \(0.31\overline{2}\)
Explanation opens after your attempt
Correct Answer
C. \(0.\overline{312}\)
Step 1
Concept
The whole block (312) is repeating. So the bar will be placed over the whole (312).
Step 2
Why this answer is correct
The correct answer is C. \(0.\overline{312}\). The whole block (312) is repeating. So the bar will be placed over the whole (312).
Step 3
Exam Tip
(312) का पूरा समूह दोहर रहा है। इसलिए बार पूरे (312) पर लगाया जाएगा।
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यदि (x=0.608) और (y=0.068), तो कौन-सा संबंध सही है?
If (x=0.608) and (y=0.068), which relation is correct?
#number-systems
#decimal-representation
#compare-decimals
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A (x<y)
B (x=y)
C (x>y)
D (y=1)
Explanation opens after your attempt
Step 1
Concept
The tenths digit of (0.608) is (6), while that of (0.068) is (0). Therefore, (x>y).
Step 2
Why this answer is correct
The correct answer is C. (x>y). The tenths digit of (0.608) is (6), while that of (0.068) is (0). Therefore, (x>y).
Step 3
Exam Tip
(0.608) का दसवां स्थान (6) है जबकि (0.068) का दसवां स्थान (0) है। इसलिए (x>y) है।
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सरल रूप में \( \frac{45}{150} \) का दशमलव प्रसार कैसा होगा?
In simplest form, what type of decimal expansion will \( \frac{45}{150} \) 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 निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
A. सांत / Terminating
Step 1
Concept
\( \frac{45}{150}=\frac{3}{10} \). The denominator has only (2) and (5), so the decimal will terminate.
Step 2
Why this answer is correct
The correct answer is A. सांत / Terminating. \( \frac{45}{150}=\frac{3}{10} \). The denominator has only (2) and (5), so the decimal will terminate.
Step 3
Exam Tip
\( \frac{45}{150}=\frac{3}{10} \) है। हर में केवल (2) और (5) हैं, इसलिए दशमलव सांत होगा।
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(0.125), \( \frac{1}{9} \), (0.12) में सबसे बड़ी संख्या कौन-सी है?
Among (0.125), \( \frac{1}{9} \), and (0.12), which is the greatest number?
#number-systems
#decimal-representation
#compare-numbers
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A \( \frac{1}{9} \)
B (0.125)
C (0.12)
D तीनों बराबर हैं / All three are equal
Explanation opens after your attempt
Correct Answer
B. (0.125)
Step 1
Concept
\( \frac{1}{9}=0.111\ldots \), so (0.125) is the greatest. Convert fractions into decimals for comparison.
Step 2
Why this answer is correct
The correct answer is B. (0.125). \( \frac{1}{9}=0.111\ldots \), so (0.125) is the greatest. Convert fractions into decimals for comparison.
Step 3
Exam Tip
\( \frac{1}{9}=0.111\ldots \), इसलिए (0.125) सबसे बड़ा है। भिन्नों को दशमलव में बदलकर तुलना करें।
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भिन्न \( \frac{27}{400} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{27}{400} \)?
#number-systems
#decimal-representation
#fraction-to-decimal
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A (0.675)
B (0.0675)
C (0.0274)
D (0.40027)
Explanation opens after your attempt
Correct Answer
B. (0.0675)
Step 1
Concept
\(400\times25=10000\), so \( \frac{27}{400}=\frac{675}{10000}=0.0675 \). Convert the denominator into a power of (10) to find the decimal.
Step 2
Why this answer is correct
The correct answer is B. (0.0675). \(400\times25=10000\), so \( \frac{27}{400}=\frac{675}{10000}=0.0675 \). Convert the denominator into a power of (10) to find the decimal.
Step 3
Exam Tip
\(400\times25=10000\), इसलिए \( \frac{27}{400}=\frac{675}{10000}=0.0675 \) है। हर को (10) की घात बनाकर दशमलव निकालें।
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यदि (0.4a5>0.435), तो अंक (a) का सबसे छोटा मान क्या होगा?
If (0.4a5>0.435), what is the smallest value of the digit (a)?
#number-systems
#decimal-representation
#decimal-comparison
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The tenths digits are equal and the hundredths digit (a) must be greater than (3). So the smallest value of (a) is (4).
Step 2
Why this answer is correct
The correct answer is C. (4). The tenths digits are equal and the hundredths digit (a) must be greater than (3). So the smallest value of (a) is (4).
Step 3
Exam Tip
दसवें स्थान समान हैं और सौवें स्थान पर (a) को (3) से बड़ा होना चाहिए। इसलिए (a) का सबसे छोटा मान (4) है।
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दशमलव \(1.02002000200002\ldots\) किस प्रकार का है?
What type of decimal is \(1.02002000200002\ldots\)?
#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
The number of zeros keeps changing, so there is no fixed recurring part. 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 keeps changing, so there is no fixed recurring part. Such a decimal is non-terminating non-recurring.
Step 3
Exam Tip
इसमें शून्यों की संख्या बदलती रहती है, इसलिए कोई निश्चित आवर्ती भाग नहीं है। ऐसा दशमलव असांत अनावर्ती होता है।
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