How many decimal places will \(\frac{3}{2^4\times5^2}\) have when converted into decimal?
Answer and explanation
Correct answer: 4
The denominator is \(2^4\times5^2\). To write it with a power of 10, multiply the numerator and denominator by \(5^2\): \(\frac{3\times5^2}{10^4}=\frac{75}{10000}=0.0075\). Hence, there are 4 digits after the decimal point. Option 2 results from considering only the power of 5, but the larger exponent, 4, is needed to form \(10^4\). Exam tip: for a denominator of the form \(2^m\times5^n\), the number of decimal places is \(\max(m,n)\).
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The denominator is \(2^4\times5^2\). To write it with a power of 10, multiply the numerator and denominator by \(5^2\): \(\frac{3\times5^2}{10^4}=\frac{75}{10000}=0.0075\). Hence, there are 4 digits after the decimal point. Option 2 results from considering only the power of 5, but the larger exponent, 4, is needed to form \(10^4\). Exam tip: for a denominator of the form \(2^m\times5^n\), the number of decimal places is \(\max(m,n)\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
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