Question

express the following decimal expression into rational numbers
5th question

Answer 1

Let x = 3.17bar

Multiply by 10 on both sides because only Bar value should be there after bar,

10x = 31.7 bar

As there is one number under bar, multiply by on both sides,

100x =317.7 bar

Then, Subtract 10x from both sides,

100x - 10x = 317.7 bar - 31.7 bar


=> 90x = 286




hence, 3.17 bar = 286/90

Answer 2

Answer:

$3.1\overline{7}=\frac{143}{45}$

 

Step-by-step explanation:

Given:

$3.1\overline{7}$

We need to express the given expression in p\q form that is rational number.

let $x=3.1777...$ ..............(1)

multiply both side by 10.

$10x=10\times3.1777...$

$10x=31.7777...$ .............................(2)

Subtract (1) from (2)

$10x-x=(31.7777...)-(3.1777...)$

$9x=28.6$

$x=\frac{28.6}{9}$

$x=\frac{286}{90}$

$x=\frac{143}{45}$

Therefore, $3.1\overline{7}=\frac{143}{45}$