Question

2. Without actually performing the long-division, state 129/2^2•5^3 will have a terminating or non-terminating repeating decimal expansion.

Answer 1

Fractions or rational numbers have terminating decimal expansion if and only if their denominator can be expressed as 5^a × 2^b.

But the given number's denominator has a factor of 6^2, that is, 2^2 × 3^2.
Hence it has a non terminating decimal expansion

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Answer 2

Given:

129/2^2•5^3

To find:

Whether the given number is terminating or non-terminating repeating decimal.

Solution:

1) In a rational number if the denominator of the fraction have 2ᵃ and 5ᵇ then only we can say that the number have the terminating decimal expansion.

2) And for the non terminating the denominator can have factorization of any of the integers.

3) In this question the given number 129/2^2•5^3 have the expansion of 2 and 5 only.

So, 129/2^2•5^3 have terminating decimal expansion