 # Significant Figures and Rounding So you can stop asking “How many decimal places should I write?”

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Significant Figures and Rounding So you can stop asking “How many decimal places should I write?”

Value Value 1) 4,233 2) 220 3) 0.004 4) 1.005 5) 0.010 6) 330. 7) 2.201 How many sig. figs are there? 4 4.233 x 10 3 2 2.2 x 10 2 1 4 x 10 -3 4 4.233 x 10 3 2 2.2 x 10 2 1 4 x 10 -3 # of sig figs Sci. notation 4 1.005 x 10 0 2 1.0 x 10 -2 3 3.30 x 10 2 4 2.201 x 10 0 4 1.005 x 10 0 2 1.0 x 10 -2 3 3.30 x 10 2 4 2.201 x 10 0

Rules to Rounding Do we really need to cover this? Do we really need to cover this? 0 – 4: Round down 0 – 4: Round down 6 – 9: Round up 6 – 9: Round up 5 and some other non-zero digit(s): Round up 5 and some other non-zero digit(s): Round up 5 and no other digit: Round the previous digit to be EVEN (not odd) 5 and no other digit: Round the previous digit to be EVEN (not odd)

Why not? Why not? 1) 4,200 2) 5,220. 3) 15.10 4) 2.01 5) 0.01 6) 330 7) 2.23 8) 0.054 Answers Answers 1) 4,230 2) 5,220 3) 15.1 4) 2.00 5) 0.0100 6) 330. 7) 2.22 8) 0.0542 Write each of these to have three (3) sig figs. Round if you must. Value Value 1) 4,233 2) 5,220 3) 15.104 4) 2.005 5) 0.010 6) 330.5 7) 2.225 8) 0.05422 Answers Answers 1) 4,230 2) 5,220 3) 15.1 4) 2.00 Why not? Why not? 1) 4,200 2) 5,220. 3) 15.10

Multiplication Remember Remember (factor 1 ) x (factor 2 ) x (factor n ) = product(factor 1 ) x (factor 2 ) x (factor n ) = product Answer (product) should have the same number of sig figs as the least of the factors. Answer (product) should have the same number of sig figs as the least of the factors. Example:Example: 17.04 x 2.2 = 37.488 (from calculator) 17.04 x 2.2 = 37.488 (from calculator) (4 sig fig) x (2 sig fig)  answer with 2 sig figs (4 sig fig) x (2 sig fig)  answer with 2 sig figs 37.448  37

Multiplication (cont’d) Answer (product) should have the same number of sig figs as the least of the factors. Answer (product) should have the same number of sig figs as the least of the factors. Example:Example: 17.04 x 2.20 = 37.488 (from calculator) 17.04 x 2.20 = 37.488 (from calculator) (4 sig fig) x (3 sig fig)  answer with 3 sig figs (4 sig fig) x (3 sig fig)  answer with 3 sig figs 37.488  37.5 Only do your rounding in the FINAL STEP or you could create rounding errors.

Division Remember Remember (dividend) ÷ (divisor) = quotient(dividend) ÷ (divisor) = quotient Answer (quotient) should have the same number of sig figs as the lesser of the dividend or divisor. Answer (quotient) should have the same number of sig figs as the lesser of the dividend or divisor. Example:Example: 170 ÷ 2.25 = 75.5555 (from calculator) 170 ÷ 2.25 = 75.5555 (from calculator) (2 sig fig) ÷ (3 sig fig)  answer with 2 sig figs (2 sig fig) ÷ (3 sig fig)  answer with 2 sig figs 75.5555  76

Division (cont’d) Answer (quotient) should have the same number of sig figs as the lesser of the dividend or divisor. Answer (quotient) should have the same number of sig figs as the lesser of the dividend or divisor. Example:Example: 170. ÷ 2.25 = 75.5555 (from calculator) 170. ÷ 2.25 = 75.5555 (from calculator) (3 sig fig) ÷ (3 sig fig)  answer with 3 sig figs (3 sig fig) ÷ (3 sig fig)  answer with 3 sig figs 75.5555  75.6 Only do your rounding in the FINAL STEP or you could create rounding errors.

How many sig figs does the answer have? 10 x 2.55 10 x 2.55 100 x 25 100 x 25 100. x 25 100. x 25 24.00 / 12.0 24.00 / 12.0 480 / 4 480 / 4 22.44 / 14.2 22.44 / 14.2 (16 / 2) x 9 (16 / 2) x 9 25.5  30 25.5  30 2500  2000 2500  2000 2500  2500 2500  2500 Computations 112 2  2.00 2  2.00 120  100 120  100 1.580 28  1.58 72  70 72  703131

Put these numbers in standard notation 102.55 + 101.9 102.55 + 101.9 100.0 + 91.22 100.0 + 91.22 90 + 25.6 90 + 25.6 102.55 + 101.9 102.55 + 101.9 14,400 + 490 14,400 + 490 22.74 – 14.2 22.74 – 14.2 (16 / 2.0) + 9.0 (16 / 2.0) + 9.0 204.45  204.4 191.22  191.2 115.6  120 or 116 (Why?) 116 (Why?) Computations 204.45  204.4 14,890  14,900 18.54  18.5 18.54  18.5 8.0 + 9.0  17.0

Quiz Time Depending on the class’s behavior, it may be open-note or closed-note. So now you can stop asking “How many decimal places should I write?”

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