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Chapter 1 · Question 6

Decide whether $\frac{13}{3125}$ and $\frac{17}{6}$ have terminating decimal expansions.

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Q6

Decide whether $\frac{13}{3125}$ and $\frac{17}{6}$ have terminating decimal expansions.

Answer Revealed

Direct Answer:

For

\frac{13}{3125}

,

3125=5^5

, so it terminates. For

\frac{17}{6}

,

6=2\times3

contains prime factor

3

, so it is non-terminating recurring.

Simple Explanation

Only denominators made from

2

s and

5

s terminate.

3125

is only

5

s;

6

has a

3

.

Exam-Ready Structure

First ensure the fractions are in lowest terms.

3125=5^5

, so

\frac{13}{3125}

has a terminating decimal expansion. But

6=2\times3

, and the factor

3

is neither

2

nor

5

. Therefore

\frac{17}{6}

has a non-terminating recurring decimal expansion.

Key Points

For $\frac{13}{3125}$ , $3125=5^5$ , so it terminates.
Use the NCERT formula or theorem carefully.
Write units and final conclusion where applicable.

Related Questions

State Euclid's division lemma and explain how it is used to find the HCF of two positive integers.

Find the HCF of $135$ and $225$ using Euclid's division algorithm.

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