Without actually performing the long division state whether 17 / 3125 will have a terminating decimal expansion or a non-terminating decimal expansion

It is terminating decimal expansion.

Step-by-step explanation:

17/3125 is a terminating decimal expansion.

REASON:

If the factors of the denominator are in the form of 2^n 5^m then the rational number is a terminating decimal expansion otherwise it is recurring. Here n and m are non negative integers.

Proof:

Lets have a look on the solution of the given term.

17/1325

We will break the denominator in the factors:

If we multiply 5 five times than it will give us 1325.

17/1325 = 17/5^5 * 2^0 = 17/2^0 * 5^5

We know that any number with exponent zero = 1

∴ 2^0 = 1

So it satisfies our explanation that the factors of the denominator are in the form of 2^n * 5^m and n and m are non negative integers.

Thus this term has a terminating decimal expansion

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