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## Accuracy

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**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 • 5.7 x 103 • 7.48 x 109 • 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 • 9.82 x 10-4 • 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