Question

2.318 repeating as a mixed number

Answer 1

the answer is 2 159/200

Answer 2

2.318... =
`2(106)/(333)`

Explanation:

The given number is 2.318 repeating.

So, let's take x = 2.318318...

318 repeating after the decimal point.

So multiply x with 1000

1000x = 1000*2.318318....

1000x = 2318.318...

This can be written as

1000x = 2316 + 2.318...

We know that x = 2.318....

1000x = 2316 + x

1000x - x = 2316

999x = 2316

Dividing both sides by 999, we get

x =
`(2316)/(999)`

x =
`2(318)/(999)`

Now we can simplify the fraction form by 3, we get

x =
`2(106)/(333)`