Checking Calculations

Checking Calculations

GCSE(F) GCSE(H)

It is easy to mis-key a number into a calculator or computer. Estimates are used to check that a calculation has been carried out correctly.

An estimated answer will give the size of a number, rather than a particularly accurate answer. If an answer is estimated to be in the hundreds, and the actual answer is in the tens of thousands, then there is an issue either with the estimate or the calculation and both should be checked.

Estimates can also provide a check against errors in calculations when that calculation is carried out electronically, either from a calculator or a computer.

Examples

1. Using a calculator, Dylan worked out 35.66 x (72.44 + 32.44) = 26156.504. Without using a calculator, show that Dylan is wrong.

Answer: 35.66 x (72.44 + 32.44) ≈ 40 x (70 + 30) = 40 x 100 = 4000

The accurate answer is 3740.0208.

2. The computer in the shop indicates that there are 14,320 bars of chocolate in the store room. Amelia knows that there are 56 bars in each box; that there are 14 boxes on a shelf, and the boxes fill up three shelves. Estimate whether the computer is correct.

Answer: The computer is wrong: there are approximately 1800 bars of chocolate.

56 x 14 x 3

≈ 60 x 10 x 3

= 1800