Accuracy Rounding Rounding is a way to shorten

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Accuracy

Accuracy

Rounding • Rounding is a way to shorten numbers that have too many decimal

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

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

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.

Answers • • • 15 31 80 4. 7 30 51 73. 59 0. 31 100

Significant Figures • • • • You can also round to significant figures The

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

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

Answers • • • 660 500 0. 06 30, 300 90, 000 20, 800

Estimating • When we estimate we usually round to 1 s. f. • E.

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

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

Try these; • Write down the upper and lowers limits for these: • The length of a pencil is 16 cm 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

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.

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 10 z (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 5 x 103

Really Big Numbers • • • 4 x 106 4, 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

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, 000 378, 000

Answers • • 305 This is written wrong 9 it should be 4. 9

Answers • • 305 This is written wrong 9 it should be 4. 9 x 107 5, 700 7, 480, 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

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

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.

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