Question

Explain why 126÷125 is a terminating decimal without performing division​

Answer 1

Step-by-step explanation:

126÷125

126÷5³

It is in the form of 5 power n So 126÷125 is a terminating decimal

Answer 2

The prime factors of the denominator contain only multiple 5 or the denominator is in the form of $2^n \times 5^m$ therefore, it is terminating decimal .

Step-by-step explanation:

Consider the provided information.

We need to determine why 126÷125 is a terminating decimal.

Make the prime factor of denominator.

$\dfrac{126}{125}=\dfrac{126}{5\times5\times5} =\dfrac{126}{5^3}$

Denominator is 5³ which is in the form $2^n \times 5^m$

Where n = 0 and m = 3

If the prime factors of the denominator contain 2 or 5 or both then it is terminating decimal otherwise non-terminating.

Here, the prime factors of the denominator contain only multiple of 5, that means the decimal expansion of the fraction is terminating.

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