Making estimates

Rounding prices

Imagine that you are buying a T-shirt for \pounds9.99, a pair of socks for \pounds1.49 and a belt for \pounds8.99. The cashier charges you \pounds23.47. You feel that this is too much - but how do you know?

One way of finding out whether you have been over-charged is to estimate what the total amount should be. Round the different prices into easier numbers - \pounds9.99 is approximately \pounds10, \pounds1.49 is approximately \pounds1.50 and \pounds8.99 is approximately \pounds9 - and you can do the calculation quickly in your head.

\pounds{9.99} + \pounds{1.49} + \pounds{8.99} \approx \pounds{10} + \pounds{1.50} + \pounds{9} = \pounds{20.50}

This is almost \pounds3 less than the cashier asked for, so obviously you have been over-charged.

The symbol \approx means 'approximately equal to'.


By rounding the actual values to more manageable numbers, you can estimate the answers to many problems:

\pounds{2.99} + \pounds3.10 + 99p \approx \pounds{3} + \pounds{3} + \pounds{1} = \pounds{7}

29 \times 9 \approx 30 \times 10 = 300

61 \div 6 \approx 60 \div 6 = 10