Without actual division, show that each of the following rational numbers is a nonterminating repeating decimal.
$(i) \frac{29}{343} (i i) \frac{64}{455}$

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Solution

(i) We know 7 is not a factor of 29, so it is in its simplest form.

Moreover, $7^{3} \neq (2^{m} \times 5^{n})$

Hence, the given rational is non-terminating repeating decimal.

(ii) $\frac{64}{455} = \frac{64}{5 \times 7 \times 13}$

We know 5, 7 or 13 is not a factor of 64, so it is in its simplest form.

Moreover, ( $5 \times 7 \times 13) \neq (2^{m} \times 5^{n})$

Hence, the given rational is non-terminating repeating decimal.

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Similar questions

Without actual division, show that each of the following rational numbers is a nonterminating repeating decimal.

$(i) \frac{11}{(2^{3} \times 3)} (i i) \frac{73}{(2^{2} \times 3^{3} \times 5)}$

Without actual division, show that each of the following rational numbers is a nonterminating repeating decimal.

$(i) \frac{11}{(2^{3} \times 3)} (i i) \frac{73}{(2^{2} \times 3^{3} \times 5)} (i i i) \frac{129}{(2^{2} \times 5^{3} \times 7^{2})} (i v) \frac{9}{35} (v) \frac{77}{210} (v i) \frac{32}{147} (v i i) \frac{29}{343} (v i i i) \frac{64}{455}$

Q. Question 1 (iii)
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:

\frac{64}{455}

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{64}{455}$ [1 MARK]

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

\frac{64}{455}

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Without actual division, show that each of the following rational numbers is a nonterminating repeating decimal. (i) 29343 (ii) 64455

Without actual division, show that each of the following rational numbers is a nonterminating repeating decimal.
$(i) \frac{29}{343} (i i) \frac{64}{455}$