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Rounding and estimation
Rounding and estimation

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1.4.1 Try some yourself

Activity 5

Round a measurement of 1.059 metres:

  • (a) to the nearest whole number of metres;

  • (b) to two decimal places;

Answer

  • (a) 1.059 m rounded to the nearest whole number of metres is 1 m.

  • (b) 1.059 m rounded to two decimal places is 1.06 m.

Activity 6

Round each of the numbers below to:

  • (a) to 1 d.p.

  • (b) to 2 d.p.

  • (c) to 3 d.p.

  0.472 65,  13.959 943,  56.098 27

Answer

  • (a) 0.5,  14.0,  56.1

  • (b) 0.47,  13.96,  56.10

  • (c) 0.473,  13.960,  56.098

Activity 7

The table below contains some errors. Identify them and write down the correct rounding.

Rounded to
Number1 d.p.2 d.p.3 d.p.
3.141 592 63.103.143.150
22/73.13.043.142
0.019 9990.00.190.200

Answer

The corrected entries are in bold.

Rounded to
Number1 d.p.2 d.p.3 d.p.
3.141 592 63.13.143.142
22/73.13.143.143
0.019 9990.00.020.020

Activity 8

Imagine you are alone on an island and that your only source of drinking water is a wrecked ship's full water tank. It measures 4 metres long by 3.45 metres wide and is 2.84 metres high. Use reasonable rounded values to make an estimate (without using your calculator) of how long you can survive until it rains, assuming that you need 2 litres per day and that the water remains perfectly fresh. You may need the conversion 1 cubic metre contains 1000 litres. (Note that volume = length × width × height.)

Answer

Rounding to approximate accuracy and then calculating the volume of the tank by using the formula length × width × height gives a volume of approximately 4 × 3 × 3 = 36 cubic metres. 1 cubic metre contains 1000 litres, so 36 cubic metres contains 36 × 1000 = 36 000 litres.

If you need 2 litres per day of water then you can survive 36 000 ÷ 2 = 18 000 days before it rains. This is about 20 000 days and taking a year to be about 400 days means that you can survive about 20 000 ÷ 400 = 50 years.

The accurate answer would give 53.69 years (to 2 d.p.). You might not be too concerned to be told that you had only 50 years rather than 53.69 years to live on your deserted island if it did not rain!