Estimation and rounding Making estimates

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'.

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

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

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