1. Estimation Great Marlow School Mathematics Department

2. Why do we estimate? In some circumstances it is unrealistic to work out the exact answer to a problem, or you may have to check an answer. Therefore an estimate is needed. For an estimate, all numbers are rounded to one significant figure – it makes the calculation easier. Then you do the calculation with the rounded numbers. Great Marlow School Mathematics Department

3. For example… 9.7 x 3.1 Round each number to one significant figure and you get….  10 x 3 = 30 This gives you an estimate. The exact or true answer is: 9.7 x 3.1 = 30.07 Great Marlow School Mathematics Department

4. Estimate: 81.4 x 98.2 Round each number to 1 significant figure and you get…  80 x 100 = 8000 This gives you an estimate. The exact or true answer is: 81.4 x 98.2 = 7993.48 Great Marlow School Mathematics Department

5. Estimate: 17.5 x 42 1.5 Round each number to 1 significant figure and you get…  20 x 40 = 800 = 400 2 2 The exact answer is: 490 – check this with your calculator Great Marlow School Mathematics Department

6. A more difficult estimate: 33.5 + 42.4 0.0237 Estimate each number to 1 significant figure:  30 x 40 = 1200 = 60000 0.02 0.02 How did we do this division? Great Marlow School Mathematics Department

7. 1200 0.02 TThis division is difficult …. So we have to change the denominator (the number on the bottom of the fraction) into a number we can divide by. What number could we change it to? 22 So the calculation would mean making the denominator 100 times bigger… So the numerator (the number on the top) has to be 100 times bigger as well…what you do to the bottom…you must do to the top! The calculation would then be: 11200 x 100 = 120000 = 60000 0.02 x 100 2