Question

3.127bar for (7)is the bar
express the following decimal into rational form.
pls explain step by step​

Answer 1

Answer:

563 / 180

Step-by-step explanation:

Let a = 3.127 bar on 7

 Multiply both sides by 100 :

⇒ 100a = 312.7 bar    ...( 1 )

    Multiply both sides by 10:

⇒ 1000a = 3127.7 bar    ...( 2 )

     Subtract ( 1 ) from ( 2 ):

  1000a = 3127.7 bar

 - 100a = - 312.7 bar

  900a = 2815        

 ⇒ 900a = 2815

        ⇒ a = 2815/900

        ⇒ a = 563 / 180

Hence,

3.127 bar = 563 / 180

Answer 2

Let , the number be

$\sf x = 3.12 \bar{7 } \: \: or \: \: 3.12777...$

Multiply given number by 100 , we get

100x = 312.777 ... ---- (i)

Multiply eq (i) by 10 , we get

1000x = 3127.777 ... ---- (ii)

Now , subtract eq (i) from (ii) , we get

$\Rightarrow \sf 900x = 2815 \\ \\ \Rightarrow \sf x = \frac{2815}{900} \\ \\ \Rightarrow \sf x = \frac{563}{180} </p><p>$

$\therefore \sf \bold{ \underline{The \: required \: rational \: number \: is \: \frac{563}{180} }}$