Question

express the rational number 1/99 in recurring decimal form by using the rucurring decimal expansion of 1/11. hence write 100/99 is recuring decimal form

Answer 1

Answer:

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.

Now, is rewritten as

=0.03030303030303….

Now, to write in recurring decimal form.

=2.151515151515…

"

Answer 2

Answer:

$=0.0303030303030 ......331=0.0303030303030......</p><p>=2.15151515151515 ..............3371=2.15151515151515..............$

Step-by-step explanation:

$Express : The \: \: rational \: \: number \frac{1}{33}331 \: \:  in \: \: recurring \: \: decimal \: \: form \: \: by using the \: \: recurring decimal expansion of  \frac{1}{11}111 .$

Hence write  

$\frac{71}{33}3371$

 in recurring decimal form.

Solution :

First we find the rational number

$\frac{1}{11}111$

in decimal form.

$\frac{1}{11}=0.0909090909090..........111=0.0909090909090..........$

Now, 

$\frac{1}{33}331$

is re-written as

$\frac{1}{33}=\frac{1}{3}\times\frac{1}{11}331=31×111$

$\frac{1}{33}=\frac{1}{3}\times0.0909090909090........331=31×0.0909090909090........$

$\frac{1}{33}=0.0303030303030 ......331=0.0303030303030......$

Now, To write

$\frac{71}{33}3371$

 in recurring decimal form

$\frac{71}{33}=71\times\frac{1}{33}3371=71×331$

$\frac{71}{33}=71\times0.0303030303030 .......3371$

$\frac{71}{33}=2.15151515151515 ..............337$

$=2.15151515151515..............$

ANSWER✍✍