Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{129}{2^{2} {.5}^{7} {.7}^{5}}$

Open in App

Solution

$q = 2^{2} {.5}^{7} {.7}^{5}$
Therefore, denominator is not of the form $2^{n} {.5}^{m}$ , where m and n are non-negative integers.
It means rational number $\frac{129}{2^{2} {.5}^{7} {.7}^{5}}$ has non-terminating repeating decimal expansion.

Suggest Corrections

Similar questions

Q. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

129÷2²5⁷7⁵

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{6}{15}$

Join BYJU'S Learning Program

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : 12922.57.75

q=22.57.75 Therefore, denominator is not of the form 2n.5m, where m and n are non-negative integers. It means rational number 12922.57.75 has non-terminating repeating decimal expansion.

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{129}{2^{2} {.5}^{7} {.7}^{5}}$

$q = 2^{2} {.5}^{7} {.7}^{5}$
Therefore, denominator is not of the form $2^{n} {.5}^{m}$ , where m and n are non-negative integers.
It means rational number $\frac{129}{2^{2} {.5}^{7} {.7}^{5}}$ has non-terminating repeating decimal expansion.