PERCENTAGES

PERCENTAGES
Percentages are numerators of fractions with denominator 100 and have been used in
comparing results. Percent is derived from the Latin word ‘per centum’ meaning ‘per hundred’.
Percent is represented by the symbol % and means hundredths too. That is 1% means 1 out
of hundred or one hundredths. It can be written as: 1% = 1/100 = 0.01
Example:
A shop has the following number of shoe pairs of different sizes. Find the Percentage of
each shoe size available in the shop.
Size 2 : 20 | Size 3 : 30 | Size 4 : 28 | Size 5 : 14 | Size 6 : 8
How do we calculate the Percentage of an item if the total number of items do not add up to
100? In such cases, we need to convert the fraction to an equivalent fraction with
denominator 100.
Example:
Mala has a collection of bangles. She has 20 gold bangles and 10 silver bangles. What is the
percentage of bangles of each type?
Converting Fractional Numbers to Percentage
Fractional numbers can have different denominator. To compare fractional numbers, we
need a common denominator and we have seen that it is more convenient to compare if
our denominator is 100. That is, we are converting the fractions to Percentages.
Example:
Write 1/3 as percent.
We have, 1/3 x 100/100 = 1/3 x 100 x (1/100) = 100/3 % = 33 1/3 %
Example:
Convert 5/4 to percent.
We have, 5/4 × 100% = 500/4 = 125 %
Converting Decimals to Percentage
We have seen how fractions can be converted to per cents. Let us now find how decimals
can be converted to per cents.
Example:
Convert the given decimals to per cents: (a) 0.75 (b) 0.09 (c) 0.2
(a) 0.75 = 0.75 × 100 % = 75% (b) 0.09 = 9/100×100% = 9 % (c) 0.2 = 2/10 × 100% = 20 %
Converting Percentages to Fractions or Decimals