Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal:
(vii) $\frac{29}{343}$

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Solution

Solution:
When the denominator of a fraction has a factor other than the factors of the form $2^{m} \times 5^{n}$ (Where ‘m’ and ‘n’ are positive integers), then rational numbers is a non-terminating repeating decimal.
For the given rational number, we will factorize numerator and denominator as follow,
$\frac{29}{343}$ $= \frac{29}{7 \times 7 \times 7}$
As the denominator has the factors $' 7'$ other than the factors of the form $2^{m} \times 5^{n}$ .
Therefore, $\frac{29}{343}$ is a non-terminating repeating decimal.

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Similar questions

Q. Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal:

(i)

\frac{11}{(2^{3} \times 3)}

(ii)

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

(iii)

\frac{129}{(2^{2} \times 5^{7} \times 7^{5})}

(iv)

\frac{9}{35}

(v)

\frac{77}{210}

(vi)

\frac{32}{147}

(vii)

\frac{29}{343}

(viii)

\frac{64}{455}

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

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

Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal:

(v) $\frac{64}{455}$

Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal:

(iii) $\frac{9}{35}$

Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal:

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

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Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal:(vii) 29343

Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal:
(vii) $\frac{29}{343}$