Question

Convert the decimal expansion 0.370370... to a fraction.

A)

10
27
B)

11
27

C)
9
25

D)
9
28

Answer 1

The answer is A 10/27 is 0.370370..

Answer 2

`0.370370.....=(10)/(27)`

A is correct

Explanation:

We are given a repeating decimal 0.370370.......

Let,

`x=0.\overline{370}`

`x=0.370370370...`

In the given repeating decimal 3 digits repeating.

`x=0.370370370.....--------(1)`

So, we will multiply both sides by 1000

`1000x=370.370370370.....-------(2)`

Subtract eq(2) - eq(1)

`1000x-x = 370`

`999x=370`

`x=(370)/(999)`

Reduce the fraction by factor of 37

`x=(10)/(27)`

Hence, The given repeating decimal 0.370370....... as fraction
`(10)/(27)`