Decimals - Converting into Fractions

   To convert Decimal Fractions into fractions, we need to understand exactly what the decimal fraction actually means. Any number that is placed in the tenths column has a value of that number of tenths.

So 0.1 is 1/10, 0.2 is 2/10 and so on.

Any number that is placed in the hundredths column has a value of that number of hundredths.   So 0.01 is 1/100, 0.02 is 2/100 and so on.

0.13 is one tenth and three hundredths.

0.13 can also be thought of as thirteen hundredths (because 1/10 is the same as 10/100 plus the 3/100 = 13/100)

To convert a decimal to a fraction we need to divide by the number of places that the decimal occupies. If only the tenth column is used, divide by ten,
0.5 is 5 ÷ 10 or 5/10, 0.7 is 7 ÷ 10 or 7/10

If the hundredths column is used, divide by 100,
0.03 is 3 ÷ 100 or 3/100, 0.08 is 8 ÷ 100 or 8/100, 0.25 is 25 ÷ 100 or 25/100.

Next we need to simplify the fraction, by dividing the numerator and denominator
by the Highest Common Factor, HCF.

For, 0.5 ... 5/10 ... HCF is 5, divide the numerator and denominator by 5 to give 1/2.

For, 0.8 ... 8/10 ... HCF is 2, divide the numerator and denominator by 2 to give 4/5.

For, 0.75 ... 75/100 ... HCF is 25, divide the numerator and denominator by 25 to give 3/4.

To convert Fractions to Decimals,

we simply divide the numerator by the denominator.

3/4 is 3 ÷ 4 = 0.75,     1/2 is. 1 ÷ 2 = 0.5,     4/5 is 4 ÷ 5 = 0.8,     13/100 is 13 ÷ 100 = 0.13