Question

Change this number into a rational number

0.102 with a bar on 2

Answer 1

Bar is represented as underline.

Answer:

23/225

Step-by-step explanation:

Let 0.102 = x      

As we have two extra numbers after decimal, multiply both sides by 100.

⇒ 100 * 0.102 = 100 * x

⇒ 10.2 = 100x       ...(1)

   Multiply both sides by 10:

⇒ 102.2 = 1000x    ...(2)

  Subtract (1) from (2)

  102.2 = 1000x

  - 10,2 = - 100x

    92   = 900x

Bar got cancelled(or subtracted)

92 = 900x

92/900 = x

23/225 = x  = 0.102(bar)

Answer 2

let x =2.37 bar

as there are 2 numbers under bar multiply by 100

100×x=100×2.37 bar

100x=237.37 bar

-x=2.37 bar (subtract x from both sides )

99x=235 (bar will be cancel)

x=235/99

now 2.37 bar in rational form is 235/99