Question 1/5
Expert Mathematics
Real Numbers 7: Decimal expansion of rational numbers Class 10 Level 21
\(\frac{11}{2^8\cdot 5^5}\) को \(\frac{N}{10^8}\) में बदलने पर (N) क्या होगा?
When \(\frac{11}{2^8\cdot 5^5}\) is converted into \(\frac{N}{10^8}\), what is (N)?
#denominator-conversion
#powers-of-10
#numerator-adjustment
#real-numbers
A (275)
B (1375)
C (2750)
D (6875)
Explanation opens after your attempt
Step 1
Concept
Since \(10^8=2^8\cdot 5^8\), the denominator lacks \(5^3\). Thus \(N=11\cdot 125=1375\).
Step 2
Why this answer is correct
The correct answer is B. (1375). Since \(10^8=2^8\cdot 5^8\), the denominator lacks \(5^3\). Thus \(N=11\cdot 125=1375\).
Step 3
Exam Tip
\(10^8=2^8\cdot 5^8\) है इसलिए हर में \(5^3\) की कमी है। \(N=11\cdot 125=1375\) होगा।
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Question 2/5
Expert Mathematics
Real Numbers 7: Decimal expansion of rational numbers Class 10 Level 20
\(\frac{7}{2^6\cdot 5^4}\) को \(\frac{N}{10^6}\) में बदलने पर (N) क्या होगा?
When \(\frac{7}{2^6\cdot 5^4}\) is converted into \(\frac{N}{10^6}\), what is (N)?
#denominator-conversion
#powers-of-10
#numerator-adjustment
#real-numbers
A (35)
B (175)
C (700)
D (875)
Explanation opens after your attempt
Step 1
Concept
Since \(10^6=2^6\cdot 5^6\), the denominator lacks \(5^2\). Thus \(N=7\cdot 25=175\).
Step 2
Why this answer is correct
The correct answer is B. (175). Since \(10^6=2^6\cdot 5^6\), the denominator lacks \(5^2\). Thus \(N=7\cdot 25=175\).
Step 3
Exam Tip
\(10^6=2^6\cdot 5^6\) है इसलिए हर में \(5^2\) की कमी है। \(N=7\cdot 25=175\) होगा।
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Question 3/5
Expert Mathematics
Real Numbers 7: Decimal expansion of rational numbers Class 10 Level 19
\(\frac{3}{2^4\cdot 5^6}\) को \(\frac{N}{10^6}\) में बदलने पर (N) क्या होगा?
When \(\frac{3}{2^4\cdot 5^6}\) is converted into \(\frac{N}{10^6}\), what is (N)?
#denominator-conversion
#powers-of-10
#numerator-adjustment
#real-numbers
A (6)
B (12)
C (24)
D (48)
Explanation opens after your attempt
Step 1
Concept
Since \(10^6=2^6\cdot 5^6\), the denominator lacks \(2^2\). Thus \(N=3\cdot 4=12\).
Step 2
Why this answer is correct
The correct answer is B. (12). Since \(10^6=2^6\cdot 5^6\), the denominator lacks \(2^2\). Thus \(N=3\cdot 4=12\).
Step 3
Exam Tip
\(10^6=2^6\cdot 5^6\), इसलिए हर में \(2^2\) की कमी है। \(N=3\cdot 4=12\) होगा।
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Question 4/5
Hard Mathematics
Real Numbers 7: Decimal expansion of rational numbers Class 10 Level 21
\(\frac{1}{2^5\cdot 5^8}\) के हर को \(10^8\) बनाने के लिए किससे गुणा करना होगा?
By what should the denominator of \(\frac{1}{2^5\cdot 5^8}\) be multiplied to make it \(10^8\)?
#powers-of-10
#denominator-conversion
#terminating-decimal
#real-numbers
A \(2^3\)
B \(5^3\)
C \(10^3\)
D \(2^5\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\)
Step 1
Concept
\(10^8=2^8\cdot 5^8\).
Step 2
Why this answer is correct
The given denominator is \(2^5\cdot 5^8\), so it lacks \(2^3\).
Step 3
Exam Tip
To form \(10^k\), increase the prime factor with the smaller exponent. चरण 1: \(10^8=2^8\cdot 5^8\) होता है। चरण 2: दिए गए हर में \(2^5\cdot 5^8\) है, इसलिए \(2^3\) की कमी है। चरण 3: \(10^k\) बनाने के लिए कम घात वाले अभाज्य गुणनखंड को बढ़ाएँ।
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Question 5/5
Hard Mathematics
Real Numbers 7: Decimal expansion of rational numbers Class 10 Level 20
\(\frac{1}{2^4\cdot 5^6}\) के हर को \(10^6\) बनाने के लिए अंश और हर को किससे गुणा करना चाहिए?
By what should numerator and denominator of \(\frac{1}{2^4\cdot 5^6}\) be multiplied to make the denominator \(10^6\)?
#denominator-conversion
#powers-of-10
#terminating-decimal
#real-numbers
A \(2^2\)
B \(5^2\)
C \(10^2\)
D \(2^4\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\)
Step 1
Concept
\(10^6=2^6\cdot 5^6\).
Step 2
Why this answer is correct
The denominator \(2^4\cdot 5^6\) lacks \(2^2\). So multiply numerator and denominator by \(2^2\).
Step 3
Exam Tip
Complete the deficiency of the prime with the smaller exponent. चरण 1: \(10^6=2^6\cdot 5^6\) होता है। चरण 2: हर \(2^4\cdot 5^6\) में \(2^2\) की कमी है। इसलिए अंश और हर को \(2^2\) से गुणा करेंगे। चरण 3: जिसकी घात कम हो, उसी की कमी पूरी करें।
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