How to convert decimals to fractions

To convert decimals to fractions, you should know the divisibility rules, which you can find here.

Just Repeating : .57575757575757575757...

To convert a plain old repeating decimal to a fraction, you need to do a few steps.

1. Identify the repeating part.
2. Identify how many digits are in the repeating part.
3. Divide digits by a number, which is in the format of (10^n)-1, where n is the number of digits in the repeating part.
4. Simplify.

Example :

Repeating part : 57.

Digits in repeating part = 2.

57/((10^2)-1)=57/99.

Simplify : 57 & 99 are not divisible by 2 ; 57 & 99 are both divisible by 3.

(57/3)/(99/3)=19/33.

19 is a prime number ; 33 is not divisible by 19, so we are done !

Normal/Repeating : .166666666666...

To convert a normal/repeating decimal to a fraction, you need to do a few more steps.

1. Identify the repeating & normal parts.
2. Identify number of digits in normal part (a digits).
3. Identify the number of digits in the repeating part (b digits).
4. Identify normal fraction ((normal part)/(10^a)).
5. Identify repeating fraction ((repeating part)/(((10^b)-1)x10^a))).
6. Simplify both fractions.
7. Add. (a/b + c/d = (ad+bc)/(bd)) or (1/a + 1/b = (a+b)/(ab))
8. Simplify.

Example :

Repeat = 6

Normal = 1

Repeat digits = 1

Normal digits = 1

Normal fraction = 1/10^1 = 1/10

Repeat fraction = 6/(((10^1)-1)x10^1) = 6/90

1/10 = 1/10

6/90 = 1/15

(1/10) + (1/15) = 25/150

25/150 = 1/6

1/6 is a unit fraction, so we are done !

Just Normal :.125

To convert a normal decimal to a fraction, you need to do a few steps.

1. Identify how many digits there are in the decimal (a digits).
2. Identify the normal fraction. ((decimal)/(10^a))
3. Simplify.

Example :

Digits = 3

Fraction = 125/10^3 = 125/1000

Simplify : 125/1000 = 1/8

1/8 is a unit fraction, so we are done !