Home > Algebra > Conversion of Decimals, Fractions, and Percent

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

Answer 1

#x = 439/999#

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#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eva Abramson

To convert the repeating decimal 0.439 (with 439 repeating) to a fraction:

Let x = 0.439439...

Multiply both sides of the equation by 1000 to move the decimal point three places to the right:

1000x = 439.439439...

Now, subtract the original equation from the new one:

1000x - x = 439.439439... - 0.439439...

999x = 439

Divide both sides by 999:

x = 439 / 999

Therefore, 0.439 (with 439 repeating) is equal to 439/999 as a fraction.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.