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Class 10MathematicsReal NumbersDecimal expansion of rational numbersMediumLevel 21
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If the decimal expansion of (\frac{5}{2^x\times5^3}) terminates exactly after (6) places, what can be the value of (x)?

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Answer and explanation

Correct answer: (6)

Step 1: The number of places is decided by the larger exponent of (2) and (5). Step 2: The exponent of (5) is (3), so for exactly (6) places the exponent of (2) must be (6). Step 3: Match the larger exponent with the required decimal places.

Related tags

ExponentsTerminating DecimalsDecimal Places

Frequently asked questions

What is the correct answer to this question?

(6)

Why is this the correct answer?

Step 1: The number of places is decided by the larger exponent of (2) and (5). Step 2: The exponent of (5) is (3), so for exactly (6) places the exponent of (2) must be (6). Step 3: Match the larger exponent with the required decimal places.

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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