Question

Express the rational number 1\33 in recurring decimal form by using the recurring decimal expansion of 1\11 . Hence write 71\33 in recurring decimal form.

Answer 1

Answer:

$\frac{1}{33}=0.0303030303030 ......$

$\frac{71}{33}=2.15151515151515 ..............$

Step-by-step explanation:

Express : The rational number $\frac{1}{33}$ in recurring decimal form by using the recurring decimal expansion of  $\frac{1}{11}$ .

Hence write  $\frac{71}{33}$ in recurring decimal form.

Solution :

First we find the rational number $\frac{1}{11}$ in decimal form.

$\frac{1}{11}=0.0909090909090..........$

Now, $\frac{1}{33}$ is re-written as

$\frac{1}{33}=\frac{1}{3}\times\frac{1}{11}$

$\frac{1}{33}=\frac{1}{3}\times0.0909090909090........$

$\frac{1}{33}=0.0303030303030 ......$

Now, To write $\frac{71}{33}$ in recurring decimal form

$\frac{71}{33}=71\times\frac{1}{33}$

$\frac{71}{33}=71\times0.0303030303030 .......$

$\frac{71}{33}=2.15151515151515 ..............$

Answer 2

"Solution:

The rational number is the numerator integer upon the denominator. Only integer number should be in both numerator and denominator.

First we find the rational number 1/11 in decimal form.

$\frac{1}{11}=0.0909090909..$

Now, $\frac{1}{33}$is rewritten as

$\frac{1}{33} = \frac{1}{3} \times \frac{1}{11}$

$=0.333333333.. \times 0.0909090909..$

=0.03030303030303….

Now, to write $\frac{71}{33}$ in recurring decimal form.

$\frac{71}{33} = 71 \times \frac{1}{33}$

$=71 \times 0.03030303030303..$

=2.151515151515…

$\frac{71}{33} =2.151515151515..$"