Question

How do you convert 0.45 (45 repeating) to a fraction?

Answer 1

`0.454545... = 45/99 = 5/11`

Explanation:

Short cut: `(" write down the recurring digits")/("write a 9 for each recurring digit")`

Long Method:

`"Let" x = 0.454545....`
`100x = 45.454545..... " 2 recurring digits" rArr xx 100`

`99x = 45.000000..... " the decimals all subtract to 0"`

`x = 45/99`

Simplify if possible.

Answer 2

You have to write a systems of equations, in one variable, to represent this problem.

`100x = 45.bar(45)`
`x = 0.bar(45)`

Now, subtract, like you would do to solve a systems of equations by elimination.

`99x = 45`

`x = 45/99`

`x = 5/11`

Therefore, `0.bar(45)` as a fraction is `5/11`

Hopefully this helps!