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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 0.751 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. 0.751001100=75100 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

75100÷2525=34dfrac{75}{100} div dfrac{25}{25} = dfrac{3}{4}

Examples

Converting Decimals to Fractions (Example #1)

0.0470.047
We can write 0.047=4710000.047 = \dfrac{47}{1000}, meaning 47 hundredths

Converting Decimals to Fractions (Example #2)

0.60.6
We can write 0.6=6100.6 = \dfrac{6}{10}, meaning 6 tenths

Converting Decimals to Fractions (Example #3)

0.1110.111
We can write 0.111=11110000.111 = \dfrac{111}{1000}, meaning 111 thousandths

Converting Decimals to Fractions (Example #4)

0.450.45
We can write 0.45=451000.45 = \dfrac{45}{100}, meaning 45 hundredths

Converting Decimals to Fractions Worksheets (PDF)

Converting Fractions to Decimals Worksheet 1

Converting Fractions to Decimals Worksheet 2

Converting Fractions to Decimals Worksheet 3

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