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) $\frac{329}{400}$

To do:

We have to write the given terms in decimal form and mention the type of decimal form.

Solution:

Rational numbers in their decimal representation can be classified into two categories. 

The first is terminating decimals where the digits terminate and the second is recurring decimals where the digits keep repeating after regular intervals.

(i) $\frac{36}{100}$

$\frac{36}{100} = 0.36$

$\frac{36}{100}$ has a terminating decimal expansion. 

(ii) $\frac{1}{11}$

$\frac{1}{11}  = 0.090909.....$

$\frac{1}{11}$  has a non-terminating but recurring decimal expansion.

(iii) $4 \frac{1}{8}$ 

$4 \frac{1}{8}   = \frac{(4\times 8+1)}{8}$

$= \frac{(32+1)}{8}$

$= \frac{33}{8}$

$\frac{33}{8}$

$= 4.125$

$\frac{33}{8}$ has a terminating decimal expansion.

(iv) $\frac{3}{13}$

$\frac{3}{13}=0.230769231......$

$\frac{3}{13}$ has a non-terminating non-recurring decimal expansion.

(v) $\frac{2}{11}$

$\frac{2}{11} =0.181818....$

$\frac{2}{11}$ has a non-terminating but recurring decimal expansion. 

(vi) $\frac{329}{400}$

$\frac{329}{400}=0.8225$

$\frac{329}{400}$ has a terminating decimal expansion.

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Updated on: 10-Oct-2022

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