Write the following in decimal form and say what kind of decimal expansion each has:

(i) \( \frac{36}{100}\)

(ii) \( \frac{1}{11}\)

(iii) \( 4\frac{1}{8}\)

(iv) \( \frac{3}{13}\)

(v) \( \frac{2}{11}\)

(vi) \( \frac{329}{400}\)

Asked by Vishal kumar | 1 year ago |  259

1 Answer

Solution :-

(i) \( \frac{36}{100}\)

On dividing 36 by 100, we get

Therefore, \( \frac{36}{100}=0.36,\) which is a terminating decimal.

(ii) \( \frac{1}{11}\)

On dividing 1 by 11, we get

We observe that while dividing 1 by 11, the quotient = 0.09 is repeated.

Therefore, \( \frac{1}{11}=0.0909...\) or \( \frac{1}{11}=0.\overline{09}\), which is a non-terminating and recurring decimal.

(iii) \( 4\frac{1}{8}=4+\frac{1}{8}=\frac{32+1}{8}=\frac{33}{8}\)

On dividing 33 by 8, we get

while dividing 33 by 8, the remainder is 0.

Therefore, \( 4\frac{1}{8}=\frac{33}{8}=4.125,\) which is a terminal decimal.

(iv) \( \frac{3}{13}\)

On dividing 3 by 13, we get

while dividing 3 by 13 the remainder is 3, which will continue to be 3 after carrying out 6 continuous divisions.

Therefore, \( \frac{3}{13}=0.230769....\) or \( \frac{3}{13}=0.\overline{230769}\), which is a non-terminating and recurring decimal.

(v) \( \frac{2}{11}\)

On dividing 2 by 11, we get

We can observe that while dividing 2 by 11, first the remainder is 2 then 9, which will continue to be 2 and 9 alternately.

Therefore, \( \frac{2}{11}\) = 0.1818..... or \( \frac{2}{11}\) = \( 0.\overline{18},\) which is a non-terminating and recurring decimal.

(vi) \( \frac{329}{400}\)

On dividing 329 by 400, we get

While dividing 329 by 400, the remainder is 0.

Therefore, \( \frac{329}{400}=0.8225,\) which is a terminating decimal.

Answered by Shivani Kumari | 1 year ago

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