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3 years ago

How do you convert 0.580 (80repeating) as a fraction?

Mathematics

2 answers:

Stella [2.4K]3 years ago

7 0

9514 1404 393

Answer:

115/198

Step-by-step explanation:

The repeat is 2 digits, so you can multiply the number by 10 to that power.

x = 0.58080...(2-digit repeat)

100x = 58.08080...(2-digit repeat)

Then subtract the original number.

100x -x = 99x = 58.08080... -0.58080... = 57.5

Now, divide by the coefficient of x.

x = 57.5/99 = 115/198

This fraction cannot be reduced, so is the fraction you're looking for.

0.580...(2-digit repeat) = 115/198

_____

<em>Additional comment</em>

The number of 9s in the denominator is the number of repeating digits. If the repeat started at the decimal point, the fraction would be those two repeating digits divided by two 9s (99).

Your number can be considered to be ...

0.58080...(2-digit repeat) = 0.5 + 0.0808...(2-digit repeat)

This will be ...

0.58080... = 1/2 + 8/99 = 99/198 +16/198 = 115/198

Gnom [1K]3 years ago

6 0

Answer:

58/100

Step-by-step explanation:

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