Question

How do you convert 0.439 (439 repeating) to a fraction?

Answer 1

`x = 439/999`

Explanation:

Let `x = 0.bar439" [1]"`

NOTE: If we had non-repeating numbers to the right of the decimal, we would multiply by powers of 10, until only repeating numbers were to the right of of the decimal, but we do not, therefore, we do nothing to equation [1] and proceed to the next step.

Multiply by powers of 10 until one complete repetition is to the left of the decimal:

`1000x = 439.bar439" [2]"`

Subtract equation [1] from equation [2]:

`1000x - x= 439.bar439-0.bar439`

`999x = 439`

Divide both sides by 999:

`x = 439/999`

Check with a calculator

`x = 0.bar439`