A brief instructable to making rational decimals into fractions.

Step 1: Rational Decimals?

A rational number is a number that can be made into a fraction.

Irrational numbers cannot.
Irrational numbers include:

pi 3.141529........

e (don't worry about this kids, but yes, e is the number 2.71828182845904523536028747135266... approximately)

the square root of 2 (sounds harmless enough)

numbers with increasing patterns ie 0.1212212221222212222212222221222222212222222212.....

Irrational numbers cannot be made into fractions because they are non-repeating and continue infinitely. Make sense?

Step 2: Basic Decimals

To put it basically, you just remove the "0." at the beginning, and put it over 10^a. "a" being the number of decimal places in the decimal. This means that if there are four numbers after the decimal, you put it over a 1 then four 0's, or 10 000.

0.3
=3/10
0.25
=25/100
=1/4

If there is a number in the place of the zero before the decimal, you multiply it by the denominator. This number is then added to the numerator.

3.47
=((3x100)+47)/100
=347/100

Or in other words, you move the decimal two places to the right, literally. (see the second picture)

Step 3: Repeating Decimals

For a repeating Decimal, the repeating portion is put over as many nines as the are decimal places before is repeats.
0.3333333........
=3/9
=1/3

this can be shown algebraically:
10x=0.333333333..........
9x=3
x=3/9
x=1/3

or

1000x=0.125125125125125125125..........
999x=125
x=125/999