Accuracy

Rounding Rounding is a way to shorten numbers that have too many decimal places E.g. You can round 1.45 to the nearest whole number This is 1 You can round to 1 decimal place This is 1.5

The Rules You round (the last number we keep) up if the cut off number is 5 or above E.g. 1.5 to the nearest whole number is 2 (5 was the cut off number) The number we keep stays the same if the cut off number is under 5 E.g. 1.44 to 1 d.p. Is 1.4

Try these; Round these to the nearest whole number; 14.85 30.6 79.5 Round these to 1 d.p. 4.682 29.950 50.97 Round these to 2 d.p. 73.592 0.3081 99.999

Answers 15 31 80 4.7 30 51 73.59 0.31 100

Significant Figures You can also round to significant figures The rules are: The first number is significant unless it is 0 If it is 0 then the first number that isn’t 0 is the first significant figure E.g. What is the first significant figure for these numbers 37.8 3 0.0538 5 0.002004 2 What is 37.8 to 1 s.f.? 40 (the 3 is rounded because of the 7)

Try these Round these to 2 s.f. 657 499 0.05982 Round these to 3 s.f. 30303 89950 20785

Answers 660 500 0.06 30,300 90,000 20,800

Estimating When we estimate we usually round to 1 s.f. E.g. What is 93 x 11 90 x 10 900 What is 250 x 123 300 x 100 3,000

Upper and Lower Limits When we measure things they have been rounded up or down E.g. A metre ruler is usually correct to 100.0 or 4 s.f. It could be as big as: 100.05 (this is 100.04999999 rounded to 5 s.f.) You add 5 on to the end of the number for the upper limit It could be as small as: 99.95

Try these; Write down the upper and lowers limits for these: The length of a pencil is 16cm correct to the nearest cm. The weight of a box is 23.6 lbs correct to 1 d.p. The weight of a baby is 4.2 kg correct to 1/10 of a kg A journey took 75 minutes correct to the nearest minute

Answers 15.5 to 16.5 cm 23.65 to 23.55 lbs 4.25 to 4.15 kg 75.5 minutes to 74.5 minutes

Standard Form This is a quick way of writing really long numbers e.g. a googol is 10 with 100 zeros after is but it can be written as 1 x 10100 There are rules for using standard form; It has to be written as y x 10z (this is the Exp button on your calculator) Y has to be between 1 and 10 The z tells you how many numbers come after the first number

Really Big Numbers 4 x 106 4,000,000 5 x 103 5,000 5.1 x 103 5,100 1.745 x 104 17,450 1.745 x 102 174.5 11 x 103 This is written wrong and should be 1.1 x 104

Try these; Write these as ordinary numbers; 3.05 x 102 49 x 106 Write these in standard form; 70,000 450,000 10,000,000,000 378,000,000

Answers 305 This is written wrong 9it should be 4.9 x 107 5,700 7,480,000,000 7 x 104 4.5 105 1 x 1010 or 10 x 109 3.78 x 108

Really Small Numbers Standard form can be used for really small numbers like the mass of an atom or the size of a cell etc. Decimals are written as 10-z E.g. 7.8 x 10-3 This is 0.0078 There are three zeros before the 78

Try these; Write these as an ordinary number; 2.6 x 10-3 5.7 x 10-5 Write these numbers in standard form; 0.006 0.035 0.00056 0.0006082

Answers 0.0026 0.000057 0.000982 6 x 10-3 3.5 x 10-2 5.6 x 10-4 6.082 x 10-4