Contributed by:

The percentage of the number is expressed as a fraction of 100. It is denoted by %. Also, this includes converting a decimal to a percentage, and to convert a percentage to a decimal.

1.
The use of percentages is common place in many aspects of commercial life. Interest rates, discounts,

pay rises and so on are all expressed using percentages. This leaﬂet revises the meaning of the term

‘percentage’ and shows how to calculate percentages, and how to convert expressions involving

percentages into alternative forms.

Any fraction which has a denominator of 100 can be written in a special way known as a percentage.

The symbol for percentage is %.

20

For example, the fraction 100

is written as 20%, and this is read as ‘twenty per cent’.

To convert a decimal to a percentage:

The decimal should ﬁrst be expressed as a fraction. Consider the following examples:

6

The decimal 0.06 can be written 100

which now has a denominator of 100. Thus 0.06 = 6%.

1 10

The decimal 0.1 can be written as 10 , or equivalently 100 . Thus 0.1 = 10%.

125

The decimal 0.125 can be written as 1000 , or equivalently 12.5

100

. Thus 0.125 = 12 12 %.

Convert the following decimals to percentages:

(a) 0.09, (b) 0.8, (c) 0.15, (d) 4.5, (e) 0.08, (f) 0.175.

(a) 9%, (b) 80%, (c) 15%, (d) 450%, (e) 8%, (f) 17 12 %.

To convert a percentage to a decimal:

x

This is straightforward. Simply note that x% means 100

. It may be appropriate to then re-write

this fraction in its simplest form.

For example:

25

25% = 100

. The simplest form of this fraction is obtained by cancelling down to 14 .

To convert a fraction to a percentage:

Simply multiply the fraction by 100 and relabel the result as a percentage:

For example:

3

The fraction 4

is expressed as a percentage as follows:

3 100 300

× = = 75

4 1 4

business www.mathcentre.ac.uk

c mathcentre May 29, 2003

pay rises and so on are all expressed using percentages. This leaﬂet revises the meaning of the term

‘percentage’ and shows how to calculate percentages, and how to convert expressions involving

percentages into alternative forms.

Any fraction which has a denominator of 100 can be written in a special way known as a percentage.

The symbol for percentage is %.

20

For example, the fraction 100

is written as 20%, and this is read as ‘twenty per cent’.

To convert a decimal to a percentage:

The decimal should ﬁrst be expressed as a fraction. Consider the following examples:

6

The decimal 0.06 can be written 100

which now has a denominator of 100. Thus 0.06 = 6%.

1 10

The decimal 0.1 can be written as 10 , or equivalently 100 . Thus 0.1 = 10%.

125

The decimal 0.125 can be written as 1000 , or equivalently 12.5

100

. Thus 0.125 = 12 12 %.

Convert the following decimals to percentages:

(a) 0.09, (b) 0.8, (c) 0.15, (d) 4.5, (e) 0.08, (f) 0.175.

(a) 9%, (b) 80%, (c) 15%, (d) 450%, (e) 8%, (f) 17 12 %.

To convert a percentage to a decimal:

x

This is straightforward. Simply note that x% means 100

. It may be appropriate to then re-write

this fraction in its simplest form.

For example:

25

25% = 100

. The simplest form of this fraction is obtained by cancelling down to 14 .

To convert a fraction to a percentage:

Simply multiply the fraction by 100 and relabel the result as a percentage:

For example:

3

The fraction 4

is expressed as a percentage as follows:

3 100 300

× = = 75

4 1 4

business www.mathcentre.ac.uk

c mathcentre May 29, 2003

2.
3

Then, relabelling this as a percentage, 4

= 75%.

Convert the following fractions to percentages:

(a) 38 , (b) 45 , (c) 18 , (d) 22

30

, (e) 35 , (f) 3

10

, (g) 49

50

.

(a) 37.5%, (b) 80%, (c) 12.5%, (d) 73 13 %, (e) 60%, (f) 30%, (g) 98%.

Finding a percentage of a quantity

To ﬁnd, say, 15% of 250, convert the percentage to a fraction, and remember that ‘of’ means

15 250 3750

× = = 37.5

100 1 100

To ﬁnd, say 17 12 % of 350,

17.5 350 6125

× = = 61.25

100 1 100

Find (a) 17 12 % of 275, (b) 25% of 3750, (c) 33 13 % of 936, (d) 156% of 19.5.

(a) 48.125, (b) 937.5, (c) 312, (d) 30.42.

Some simple rules

Calculating 10% of a quantity is easy. Simply move the decimal point one place to the left. Thus

10% of 1275 is 127.5. Multiples of this are easily found. For example 20% of 1275 will be 2 × 10%,

that is 2 × 127.5 = 255.

Consider the following calculation of 17.5% of 650:

10% of 650 = 65.

1

5% of 650 = 32.5.

2 % of 650 = 16.25

2

1

Putting these results together: 17 2 % of 650 is 65+32.5+16.25=113.75.

Use this method to ﬁnd, without a calculator, (a) 17.5% of 2500, (b) 30% of 62.

(a) 437.5, (b) 18.6

business www.mathcentre.ac.uk

c mathcentre May 29, 2003

Then, relabelling this as a percentage, 4

= 75%.

Convert the following fractions to percentages:

(a) 38 , (b) 45 , (c) 18 , (d) 22

30

, (e) 35 , (f) 3

10

, (g) 49

50

.

(a) 37.5%, (b) 80%, (c) 12.5%, (d) 73 13 %, (e) 60%, (f) 30%, (g) 98%.

Finding a percentage of a quantity

To ﬁnd, say, 15% of 250, convert the percentage to a fraction, and remember that ‘of’ means

15 250 3750

× = = 37.5

100 1 100

To ﬁnd, say 17 12 % of 350,

17.5 350 6125

× = = 61.25

100 1 100

Find (a) 17 12 % of 275, (b) 25% of 3750, (c) 33 13 % of 936, (d) 156% of 19.5.

(a) 48.125, (b) 937.5, (c) 312, (d) 30.42.

Some simple rules

Calculating 10% of a quantity is easy. Simply move the decimal point one place to the left. Thus

10% of 1275 is 127.5. Multiples of this are easily found. For example 20% of 1275 will be 2 × 10%,

that is 2 × 127.5 = 255.

Consider the following calculation of 17.5% of 650:

10% of 650 = 65.

1

5% of 650 = 32.5.

2 % of 650 = 16.25

2

1

Putting these results together: 17 2 % of 650 is 65+32.5+16.25=113.75.

Use this method to ﬁnd, without a calculator, (a) 17.5% of 2500, (b) 30% of 62.

(a) 437.5, (b) 18.6

business www.mathcentre.ac.uk

c mathcentre May 29, 2003