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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 19
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A fraction in lowest form is (\frac{p}{2^3\cdot 5^5}). If it is written as (\frac{N}{10^5}), what is (N)?

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Answer and explanation

Correct answer: (4p)

Step 1: We need (10^5=2^5\cdot 5^5). Step 2: The denominator (2^3\cdot 5^5) lacks (2^2). So multiply numerator and denominator by (2^2=4). Hence (N=4p). Step 3: To make (10^k), multiply by the missing prime power.

Related tags

Powers-Of-10Numerator-AdjustmentTerminating-DecimalReal-Numbers

Frequently asked questions

What is the correct answer to this question?

(4p)

Why is this the correct answer?

Step 1: We need (10^5=2^5\cdot 5^5). Step 2: The denominator (2^3\cdot 5^5) lacks (2^2). So multiply numerator and denominator by (2^2=4). Hence (N=4p). Step 3: To make (10^k), multiply by the missing prime power.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Decimal expansion of rational numbers.

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