Question

Can someone explain me how to determine whether a fraction is terminating or non terminating decimal expansion ??

Answer 1

If you see numbers that are not repeating and are not same and go on for example:-π whose value is 3.14.......... and it never ends then such fractions are known as non terminating fractions.

The fractions for example 36/5=7.2 whose decimal expansion ends are called terminating fractions.

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Answer 2

Answer:

If the prime factorization of the denominator contains all 2's and 5's then the decimal expansion of the fraction will be terminating else non-terminating.

Step-by-step explanation:

(i)

13/3125

Factorize the denominator, we get

⇒ 3125 = 5 * 5 * 5 * 5 * 5

            = 5⁵

            = 1 * 5⁵

            = 2⁰ * 5⁵.

Here, denominator is in the form of 2^n * 5^m.

Therefore, it is a terminating decimal expansion.

(ii)

29/343

Factorize the denominator, we get

⇒ 343 = 3 * 3 * 3 * 3 * 3

           = 3⁵.

It cannot be written in the form of 2^n * 5^m

Therefore, it is a non-terminating decimal expansion.

Hope it helps!