Approximation Involving the Four Basic Operations

Addition:

Worked Example 12.6.1:

What is the approximated answer to each of the following addition problems? 

i. 708   +   194
ii. 57.6   +   83.9

Solution

Round each number to 1 s.f or to the nearest 100. We have

i. 708   +  194     ≈     700   +   200    =    900

ii. 57.6   +   83.9   ≈      60   +   80   =    140

Subtraction:

Worked Example 12.6.2:

Round off each number to 1 s.f.

i. 3072 – 1365
ii. 595.845 –  96.869

Solution

i. Round each number to 1 s.f or to the nearest 1000, we have 

3072   –   1365   ≈    3000   –   1000

= 2000

ii. Round each number to 1 s.f

595.845  –  96.869

≈   600  –   100   =  500

Multiplication:

Worked Example 12.6.3:

Find the approximate answer to: 

i. 442    ×    97
ii. 4.50   ×   8.59   ×  0.75

Solution

Round each number to 1 s.f.

i. 442   ×    97   ≈    400   ×  100   =  40 000.

ii. 450   ×   8.59   x  0.75   ≈   500   ×  9   ×  1  = 4500

Division:

Worked Example 12.6.4:

Find the approximate answer to 19.56  ÷  4.85.

Solution

19.56  ÷ 4.85.   ≈    20 ÷   5  =   4

Worked Example 12.6.5:

How many 35p bags can be bought with €16.84? Round the cost to the nearest 10p.
€1 = 100p

Solution

€16.84  =  1684 p (€1 = 100p)

No of bags =  1684  ÷   35    ≈   1680  ÷   40

= 42 bags.