Question

solve the issue of maths ​

Answer 1

Given

some of no in decimal

1. $0.3\bar{2}$
2. $0.12\bar{3}$
3. $0.003\bar{52}$

To Find

the following decimal in $\frac{p}{q}$

Solution

1.)

$0.3\bar{2}$

0.322222

Let x= 0.32222____(1)

multiply by 10

=>10x=3.2222 ______(2)

multiply by 100

=>100x=32.222____(3)

Now subtracting equation (2) and (3)

99x=29

X=$\frac{29}{99}$

(2).

$0.12\bar{3}$

0.123333..

Let x= 0.123333____(1)

multiply by 10

=>10x=1.23333 ______(2)

multiply by 100

=>100x=12.33333____(3)

multiply by 1000

=>1000x=123.3333_&&&(4)

Now subtracting equation (3) and (4)

=>900x=111

X=$frac{111}{900}$

(3)

$0.003\bar{52}$

0.003525252

let x=0.0035252(.)

• Multiply by 10

10x=0.035252___(1)

• multiply by 100

100x = 0.35252_____(2)

• multiply by 1000

1000x=3.525252_____(3)

• multiply by 10000

10000=35.5252___(4)

From equation (4) and (3)

9000x=33

${\therefore}x=\frac{33}{9000}$