How do you change 0.585858 into a fraction in simplest terms?

Question

Can you please show it STEP by STEP!

Answer 1

Did you mean for there to be a "..." at the end of the decimal? If so, then using the same method as Niks, but with a minor modification:

Let x = .5858...
Then 100x = 58.5858... so 100x - x = 58, so (100 - 1)x = 58. Simplifying and dividing both sides by 99, gives x = 58/99

Answer 2

It depends on what you mean by 0.585858. Is it just that number, or does it keep repeating 5858585858... forever? (Sometimes this is indicated by putting a bar over the numbers, to show that it repeats.)

If it's just 0.585858, the way you do this is by counting the number of digits after the decimal point (there are 6), and then writing down that number of zeroes. Then put a 1 in front of the zeroes, and put the 6 digits on top. This gives you:
585858
-------------
1000000

Then you use your normal techniques to reduce the fraction.

If it's a sequence that keeps repeating, then you take the smallest part of the sequence that repeats. In this case, it's the sequence 58 that keeps repeating forever. Count the number of digits in the number (there are 2), and write down that many 9's. Then put the repeating part on top in a fraction. This will give you:
58
----
99

Again, you will reduce the fraction if possible. In this case, the fraction is already reduced.

Answer 3

i always try dividing by 9, 99, or 11

if the repeating numbers are only using 1 number once, then divide by 9, if it has 2 repeating numbers then use 99, etc... if that doesn't work, try using 11

AN S: (58/99)

Answer 4

let
x=0.585858
100x=58.5858

Subtracting 1 from 2,

99x=57.999942
x=57.999942/99

x = 57999942 / 99000000