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

##### 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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