Fractions as Decimals & Percentages
fractions as decimals  recurring decimals  handy fractions to remember
Fractions as decimals
Any fraction can be expressed as a decimal. Some are very simple to
write, others are harder, since they may not ever end. The first digit
after the decimal point is the tenths, the second digit after the decimal
point is the hundredths, and so on.
^{1}⁄_{10} = 0.1
^{1}⁄_{100} = 0.01
^{11}⁄_{100} = 0.11
^{377}⁄_{400} = 0.9425
Unfortuataly not all fractions have a multiple of 10 on the bottom line,
but there are still many that can be easily written.
^{1}⁄_{2} = 0.5
^{1}⁄_{20} = 0.05
^{1}⁄_{5} = 0.2
^{1}⁄_{50} = 0.02
^{1}⁄_{4} = 0.25
^{1}⁄_{40} = 0.025
^{377}⁄_{400} = 0.9425
Recurring decimals
If a decimal repeats is it known as a recurring
decimal. If the recurring decimal has only one digit that recurs
the number can be written with a dot (or line) above the digit. Other numbers
that have several numbers that recur can be written with a dot above
the first and last digits in the group that recurs (or a line above the whole sequence/pattern).
^{1}⁄_{3} = 0.333333...
^{1}⁄_{7} = 0.142857142857...
^{1}⁄_{7} 
=
0. 
. 

. 
1 
4285 
7 

What happens when we add three thirds?
^{1}⁄_{3} = 0.333333...
3 x ^{1}⁄_{3} = ^{3}⁄_{3}
= 1
3 x 0.333... = 0.999...
Does this means that 0.999999... ("zero point nine recurring") is
the same as 1? (Answer on the Number
Sets page.)
Handy fractions to remember
Some of the simple fractions pop up so often that it's very handy to remember the decimal and percentage equivalents. Recurring numbers can also be indicated by a dot above a single digit, or a dot above the first and last digits of a repeating pattern.
Fraction 
Decimal 
Percentage 
^{1}⁄_{2} 
0.5 
50% 
^{1}⁄_{3} 
0.333... or 0.3 
33⅓% 
^{1}⁄_{4} 
0.25 
25% 
^{1}⁄_{5} 
0.2 
20% 
^{1}⁄_{6} 
0.1666... or 0.16 
16⅔% 
^{1}⁄_{7} 
0.142857 
14^{2}⁄_{7}% 
^{1}⁄_{8} 
0.125 
12.5% 
^{1}⁄_{9} 
0.111... or 0.1 
11^{1}⁄_{9}% 
^{1}⁄_{10} 
0.1 
10% 
^{1}⁄_{11} 
0.0909... or 0.09 
9^{1}⁄_{11}% 
^{1}⁄_{12} 
0.08333... or 0.083 
8⅓% 
^{1}⁄_{20} 
0.05 
5% 
^{1}⁄_{25} 
0.04 
4% 
^{1}⁄_{50} 
0.02 
2% 
^{1}⁄_{100} 
0.01 
1% 
Multiples of these fractions (ie, with numbers larger than 1 as the numerator) can simply be remembered or quickly worked out by adding smaller fractions together.
^{1}⁄_{8} =
0.125 = 12.5%
^{4}⁄_{8} = ^{1}⁄_{2} = 0.5 = 50%
^{5}⁄_{8} = ^{1}⁄_{8} + ^{4}⁄_{8} = 0.125 + 0.5 = 0.625 = 62.5%
^{7}⁄_{12} = ^{6}⁄_{12} + ^{1}⁄_{12} = = ^{1}⁄_{2} + ^{1}⁄_{12} = 0.5 + 0.083 = 0.583 = 58.3%
Some fractions can be worked out by multiplying the basic fractions.
^{1}⁄_{15} = ^{2}⁄_{30} = ^{2}⁄_{10} x ^{1}⁄_{3} = ^{2}⁄_{10} x 0.3 = ^{1}⁄_{10} x 0.6 = 0.06
The sevenths fractions are a little curious because each one has the same digits in its repeating decimal sequence, but starts at a different digit in the sequence.
^{1}⁄_{7} =
0.142857 = 14^{2}⁄_{7}%
^{2}⁄_{7} =
0.285714 = 28^{4}⁄_{7}%
^{3}⁄_{7} =
0.428571 = 42^{6}⁄_{7}%
^{4}⁄_{7} =
0.571428 = 57^{1}⁄_{7}%
^{5}⁄_{7} =
0.714285 = 71^{4}⁄_{7}%
^{6}⁄_{7} =
0.857142 = 85^{5}⁄_{7}%
^{7}⁄_{7} =
1 = 100%
The elevenths fractions are simply multiples of 9.
^{1}⁄_{11} =
0.09 = 9 ^{1}⁄_{11}%
^{2}⁄_{11} =
0.18 = 18 ^{2}⁄_{11}%
^{3}⁄_{11} =
0.27 = 27 ^{3}⁄_{11}%
^{4}⁄_{11} =
0.36 = 36 ^{4}⁄_{11}%
^{5}⁄_{11} =
0.45 = 45 ^{5}⁄_{11}%
^{6}⁄_{11} =
0.54 = 54 ^{6}⁄_{11}%
^{7}⁄_{11} =
0.63 = 63 ^{7}⁄_{11}%
^{8}⁄_{11} =
0.72 = 72 ^{8}⁄_{11}%
^{9}⁄_{11} =
0.81 = 81 ^{9}⁄_{11}%
^{10}⁄_{11} =
0.90 = 90 ^{10}⁄_{11}%
^{11}⁄_{11} =
1 = 100%
