What are the steps to converting .125555... into a fraction? (a repeating bar over the 5's)?

Question

What are the steps to converting .125555... into a fraction? (a repeating bar over the 5's)

Answer 1

Let x = .1255555....

Then 100x = 12.55555



100x - x = 12.55555 - .125555



=12.43



99x = 12.43



9900x = 1243



x = 1243/9900



Note: A number is rational (capable of being expressed as a fraction) if and only if its decimal expression ends in a repeating decimal. The section that repeats may be a single digit (eg. 1/3 = .3333333.... 1/2 = .50000000) or more than one digit (eg. 123/999 = .123123123123.....)

Answer 2

0.125555(repeating)



First, split the non-repeating from the repeating



0.12 + 0.005555(repeating)



Next, move the decimal place to offset the leading zeros. Divide by the appropriate multiple of 10 (if one zero, it's over 10; if two zeros, over 100).



0.12 + 0.555(repeating) / 100



Any single digit repeating decimal is represented as that number over 9. (side note: if it were two digits repeating, it would be over 99, and if three, 999.. and so forth)



0.12 + (5/9) / 100



And 0.12 is the same as 12/100



12/100 + (5/9)/100



To solve that complex fraction (the second fraction), multiply top and bottom by 9 (which is the same as multiplying by 9/9, or 1, and multiplying by 1 does not change the expression).



12/100 + 5/(9*100)

12/100 + 5/900



Solve the fraction as normal.



108/900 + 5/900



113/900



If you can plug the fraction 113/900 into your calculator, it will validate the decimal representation.

Answer 3

a repeating bar over a 5 will only simplify it in a way to let ppl kno that it is indead repeating... it is near 1/8... the closest i can get is .1255555556 which is 113/900

if it were only .125 then it would be 125/1000 which simplifies to 1/8 so if u want to do it by hand put the numberator over 1 with as many zeros as there numbers on the top. see for 125 there are 3 numbers so there are 3 zeros underneath 125/1000