2.318 repeating as a mixed number

Question

asked Sep 5, 2018 77.2k views

2 Answers

Zeratulmdq · Answer 1 · 2018-09-09T18:24:25+0000

Answer:

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)