Question

0.27 repeating as a fraction

Answer 1

0.277777777.... as a fraction is 5/18

Answer 2

Equation 1:

X= 0.27 re. (1)

Since we have 1 digits in our repeating decimal group, create a second equation by multiplying both sides 10 to the power of 1 = 10
Equation 2:

10X = 2.77 re. (2)

Subtracting equation (1) from (2)

10X = 2.77...
X = 2.77...
------------------
9X = 2.5

We get

9X = 2.5

Solving for X

X = 2.5/9

Multiplying by 1 to eliminate 1 decimal places we must multiply top and bottom by 1 10's = 10 to the first power = 10

2.5/9 times 10/10 = 25/90

Then simplify

25 divided by 5/90 divided by 5 = 5/18

In conclusion,

0.27 re. = 5/18