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Checking Calculations

Checking Calculations

It is easy to mis-key when entering 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.

Example 1

Using a calculator, Dylan worked out 35.66 x (72.44 + 32.44) = 26156.504. By using an estimate, and without using a calculator, show that Dylan is wrong.

The answer asked for the error to be shown, so show all the working.

Answer: 35.66 x (72.44 + 32.44)

≈ 40 x (70 + 30)

= 40 x 100

= 4000

Example 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.

56 x 14 x 3

≈ 60 x 10 x 3

= 1800

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