3.2 Using scientific notation
Scientific notation can be very useful when estimating the answers to calculations involving very large and/or small decimal numbers.
Example 9
A lottery winner won £7851 000. He put the money straight into a deposit account which earns 7.5% interest per annum (i.e. each year). If he wanted to live off this interest, how much per day would it be?
Answer
The amount is £7851 000 × 
÷ 365.
Estimate first to provide a check for the calculator work.
7851 000 = 7.851 × 106
8 × 106
= 7.5 × 10−2 8 × 10−2
365 = 3.65 × 102 4 × 102
So the estimate becomes:
(8 × 106) × (8 × 10−2) ÷ (4 × 102).
Now separate the digits from the powers of 10 to give:
(8 × 8 ÷ 4) × (106 × 10−2 ÷ 102).
Since 8 × 8 ÷ 4 = 16 and 106 × 10−2 ÷ 102 = 106+−2−2 = 102, the estimate is 16 × 102 = 1600 (£1600 a day!).
On a calculator, 7851 000 × 0.075 ÷ 365 gives £1613 rounded to the nearest pound, which is quite close to the estimate.