Change 0.59 repeating into a fraction? the 9 is the repeating number.

Question

0.59 (9 repeating) into  FRACTION. also 0.24 (4 repeating) into a FRACTION. I end up getting  leftover numbers and can't make it into a simple fraction. Please help me understand these problems. Thank you.

Answer 1

me thank yu want 59/99...that become 0.5959595959595959...

this thang go on forever

it yu want a LIMITED number such as 0.2424, that be 2424/10000

Answer 2

The .9 repeating after the 5 is just another way to write the number 0.6 because as 0.9 repeating is equal to 1, 0.09 repeating (just the 9) is equal to 0.1, so the decimal becomes 0.6, which is 3/5.  I'm not absolutely sure about the 0.24 though.

Answer 3

0.59999... is, in fact, 0.6 and 0.6=6/10=3/5 as a fraction.

0.244444... is a bit trickier. First, multiply by 10 and we get 2.44444...

To convert the recurring 4 into a fraction we use as many 9's as the length of the recurring part. Well, there's only one digit recurring, so we only need one 9; make a fraction of the recurring part and the 9: 4/9.

Nearly there. We had 2.44444... so that's 2 4/9. Express this is an improper fraction: 22/9 and now we must divide by 10 to compensate for multiplying by 10 earlier: 22/(9*10). This cancels a bit: 11/45, which is the fraction you're looking for.

(We can use the technique in the preceding paragraph to the first part, 0.599999... Multiply by 10 first: 5.999999, then take 9 and divide by 9: 9/9=1 so we have 5 9/9=5+1=6. Then we divide by 10: 6/10 and we get 3/5.)

Answer 4

3/5 should be your answer for the first one. The second one? Easy. Step 1: 0.24 = 24⁄100
Step 2: Simplify 24⁄100 = 6⁄25 So your second answer is 6/25