2. To convert a number written as a percentage into a rational number or a decimal, divide the number by 100.
67% = 67 ____
100 = 0⋅67 [Move the decimal point two places to the left.] 27⋅5% = 0⋅275
3. To express one quantity as a percentage of another, write the fi rst quantity as a fraction of the second and then multiply by 100%. [See Example 1.]
4. To fi nd a percentage of a quantity, multiply the quantity by the decimal equivalent of the percentage.
25% of €230 = 25 ____
5. To increase a quantity by r %, multiply it by ( 1 + r
100 × €230 = 0⋅25 × €230 = €57⋅50 ) .
____ 100
Increase 800 by 20%: 800 + 800 × 0⋅2 = 800(1 + 0⋅2) = 800 × 1⋅2 = 960 6. To decrease a quantity by r %, multiply it by ( 1 − r
____ 100
( 1 + r
____ 100
____ 100
) . [See Example 2.]
7. To fi nd a quantity which has been increased by r % to a given value, divide this given value by
) to get the original value. [See Example 3.]
8. To fi nd a quantity that has been decreased by r % to a given value, divide this given value by
( 1 – r EXAMPLE 1
32 litres (l) of oil leaked from a tank containing 160 l. What percentage of the oil leaked?
Solution
32 l out of 160 l: 32 ____
EXAMPLE 2
A piece of skirting board of length 1⋅2 m has to be reduced by 15% to fi t. What is the required length?
Solution 15% = 0⋅15
New length l = 1⋅2 – 1⋅2 × 0⋅15 = 1⋅2(1 – 0⋅15) = 1⋅2(0⋅85) = 1⋅02 m
29
160 = 1 __
5 = 1 __
5 × 100% = 20% ) to get the original value. [See Example 4.]
