
Unit 7: Numeracy skills
Percentages
Percentage is one of three ways of expressing a value, for example, 17% has the same value as 17 / 100 or 0.17
It is recommended that, before using the calculator, you first understand, through mental calculation, the principles of layout of expressions and the functions of addition, subtraction, multiplication and division in fractions and decimals.
Percentage and decimal - the relationship
Examine the ‘meaning’ of the figure 425. 631. The position of each digit gives it its value. Regard each digit as being a member of a column
hundreds | tens | ones | 1 / 10 ths | 1 / 100 ths | 1 / 1000 ths |
a | b | c | d | e | f |
4 | 2 | 5 | 6 | 3 | 1 |
Column a expresses ‘whole HUNDREDS’. b expresses ‘whole TENS.
c expresses UNITS (ONES). d. expresses 1/10ths e. expresses 1/100ths f.. expresses 1/1000ths.
1% is expressed as a fraction as 1 / 100. Hence, from the ‘column rule’, 1% is 1 in column e, so, 0.01
Try to memorise the following table. It shows how identical values are expressed in different forms – percentages, fractions and decimals
100% | = | 100 / 100 | = | 1.00 | ||
10% | = | 10 / 100 | = | 1 / 10 | = | 0.1 |
1% | = | 1 / 100 | = | 0.01 | ||
0.1% | = | 0.1 / 1000 | = | 0.001 |
Example:
Calculate 17% of 3 / 4 Give the answer as a percentage.
- Express 17% as 17 / 100
- 17% as 17 / 100 × 3 / 4 (note that ‘of’ becomes ‘ב )
- The rule of multiplication of fractions applies. Multiply the top values (numerators), and multiply the bottom values (denominators)
so, (17× 3 )/(100 × 4 ) = 51 / 400 - Approximate 51 / 400 to 50 / 400
- Simplify 50 / 400 to 1 / 8
- Convert 1 / 8 to a percentage. The principle is that the 8 (denominator) has to be converted to 100 ( in this case by multiplying by 12.5). You treat the top figure in the same way (so, 1 multiplied by 12.5 )
- You thus produce a fraction 12.5 / 100 (Remeber, you would not normally leave a fraction in this format). This indicates 12.5% as an approximate answer to the question.
- Use the calculator to find the accurate answer
- Answer 12.75%
Now try the questions on the next page!
SMILE - Numeracy skills by Tom Frank, Eric Williams and Clare Wright, University of Birmingham Careers Centre adapted by Marion Kelt Glasgow Caledonian University is licensed under a Creative Commons Attribution 3.0 Unported License.