Decimal to Fraction

A brief instructable to making rational decimals into fractions.

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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 10a. "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

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    rimar2000

    7 years ago on Introduction

    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.