## Introduction: Decimal to Fraction

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

In step 3, when you say 10x=0.333333333..........

I think you want say 10x=3.333333333.........

Well, I expected to find here a method of making any rational number into a fraction.