Question

Write the condition to be satisfied by q so that a rational number $\frac{p}{q}$ has a terminating decimal expansions.

Answer 1

SOLUTION :  

The condition to be satisfied by q so that a rational number p/q has a terminating decimal expansion must be of the form 2^m × 5ⁿ, where m and n are non negative integers.

For terminating decimal expansion Denominator of the rational number is the power of 10.

For e.g : 13/125 = 13/5³

Here, the factors of the denominator 125 are 2^0 × 5³ which is in the form 2^m 5ⁿ .

So , 13/125 has a terminating  decimal expansion.

The decimal expansion of 13/ 125 :  

13/125 = 13 ×2³ /5³× 2³

= 13 × 8 /(5×2)³

= 104 / 10³ = 104/1000  

= 0.104  

Hence, the decimal expansion of 13/125 is 0.104.

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Answer 2

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