A percentage is a fraction whose denominator is 100
(the numerator of a fraction is the top term, the denominator is the bottom
term). So 30% = 30/100 = 3/10 = 0.3 To change a decimal into a percentage,
multiply by 100. So 0.3 = 0.3 × 100 = 30% .
Example
Find 25% of 10 (remember 'of' means 'times'). 25 ×
10 (divide by 100 to convert the percentage to a decimal) 100 =
2.5
Percentage Change
% change = new value  original value × 100 original value
Example
The price of some apples is increased from 48p to 67p. By how
much percent has the price increased by? % change = 67  48 × 100 =
39.58% 48
Percentage Error
% error = error × 100 real value
Example
Nicola measures the length of her textbook as 20cm. If the
length is actually 17.6cm, what is the percentage error in Nicola's
calculation? % error = 20  17.6 × 100 = 13.64%
17.6
Original value
Original value = New value × 100 100 + %change
Example
A dealer buys a stamp collection and sells it for £2700,
making a 35% profit. Find the cost of the collection. It is the original
value we wish to find, so the above formula is used. 2700 × 100
= £2000 100 + 35
Percentage Increases and Interest
New value = 100 + percentage increase × original value
100
Example
£500 is put in a bank where there is 6% per annum interest.
Work out the amount in the bank after 1 year. In other words, the old value
is £500 and it has been increased by 6%. Therefore, new value = 106/100 × 500
= £530 .
Compound Interest
If in this example, the money was left in the bank for another year, the £530
would increase by 6%. The interest, therefore, will be higher than the previous
year (6% of £530 is more than 6% of £500). Every year, if the money is left
sitting in the bank account, the amount of interest paid would increase each
year. This phenomenon is known as compound interest. The simple way to work
out compound interest is to multiply the money that was put in the bank by
n^{m}, where n is (100 + percentage increase)/100 and m is the number of
years the money is in the bank for, i.e:
(100 + %change)^{no of
years} × original value
So if the £500 had been left in the bank for 9 years, the
amount would have increased to:
500 ×
(1.06)^{9} = £845
Percentage decreases
New value = 100  percentage decrease × original value
100
Example
At the end of 1993 there were 5000 members of a certain rare
breed of animal remaining in the world. It is predicted that their number will
decrease by 12% each year. How many will be left at the end of 1995? At the
end of 1994, there will be (100  12)/100 × 5000 = 4400 At the end of 1995,
there will be 88/100 × 4400 = 3872
The compound interest formula above can also be used for
percentage decreases. So after 4 years, the number of animals left would be:
5000 x [(10012)/100]^{4} = 2998
Copyright © Matthew Pinkney 2003
