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Converting Decimals to Fractions

Introduction

Converting a decimal to a fraction simply means to express the decimal in the form of a fraction. So in fraction form, 0.5 can be written as 50/100 (decimal fraction) or as (simplified fraction).

Terms

Decimal - A number greater than any whole number.
Fraction - A part of a whole can be expressed as a fraction.
Decimal Fraction - The un-simplified form of a fraction that has been converted from a decimal.
Simplified Fraction - A fraction that has been reduced to the lowest possible whole numbers.

Lesson

Converting a decimal to a fraction is very easy. We can express the decimal being converted as divisible by 1. So 0.75 can be written as $rac{0.75}{1}$. Now we take the number of decimal places (this particular decimal has places up to the hundredths) and multiply the top and bottom by that number. $rac{0.75 * 100}{1 * 100} = rac{75}{100}$. This is the decimal fraction. Simplifying this fraction means dividing the top and bottom by the highest common factor (in this case 25), so we get

$dfrac{75}{100} div dfrac{25}{25} = dfrac{3}{4}$

Examples

Converting Decimals to Fractions (Example #1)

$0.047$
We can write $0.047 = \dfrac{47}{1000}$, meaning 47 hundredths

Converting Decimals to Fractions (Example #2)

$0.6$
We can write $0.6 = \dfrac{6}{10}$, meaning 6 tenths

Converting Decimals to Fractions (Example #3)

$0.111$
We can write $0.111 = \dfrac{111}{1000}$, meaning 111 thousandths

Converting Decimals to Fractions (Example #4)

$0.45$
We can write $0.45 = \dfrac{45}{100}$, meaning 45 hundredths