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

58/100

Step-by-step explanation:

9514 1404 393

  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

Additional comment

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

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.