Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{29}{343}$

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Solution

$343 = 7 \times 7 \times 7$
Since denominator is not of the form $2^{n} {.5}^{m}$ , where m and n are non-negative integers.
It means rational number $\frac{29}{343}$ has non-terminating repeating decimal expansion.

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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : 29343

343=7×7×7 Since denominator is not of the form 2n.5m, where m and n are non-negative integers. It means rational number 29343 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 : $\frac{29}{343}$

$343 = 7 \times 7 \times 7$
Since denominator is not of the form $2^{n} {.5}^{m}$ , where m and n are non-negative integers.
It means rational number $\frac{29}{343}$ has non-terminating repeating decimal expansion.