Significant FiguresSignificant Figuresand Roundingand Rounding

So you can stop asking So you can stop asking “How many decimal places “How many decimal places

should I write?”should I write?”

ValueValue

1)1) 4,2334,233

2)2) 220220

3)3) 0.0040.004

4)4) 1.0051.005

5)5) 0.0100.010

6)6) 330.330.

7)7) 2.2012.201

How many sig. figs are there?How many sig. figs are there?

4 4.233 x 104 4.233 x 1033

2 2.2 x 10 2 2.2 x 1022

1 4 x 10 1 4 x 10-3-3

# of sig figs# of sig figs Sci. notationSci. notation

4 1.005 x 104 1.005 x 1000

2 1.0 x 10 2 1.0 x 10-2-2

3 3.30 x 10 3 3.30 x 1022

4 2.201 x 10 4 2.201 x 1000

Rules to RoundingRules to Rounding

Do we really need to cover this?Do we really need to cover this? 0 – 4: Round down0 – 4: Round down

6 – 9: Round up6 – 9: Round up 5 and some other non-zero digit(s): Round 5 and some other non-zero digit(s): Round

upup

5 and no other digit: Round the previous 5 and no other digit: Round the previous digit to be EVEN (not odd)digit to be EVEN (not odd)

Why not?Why not?1)1) 4,2004,2002)2) 5,220.5,220.3)3) 15.1015.104)4) 2.012.015)5) 0.010.016)6) 3303307)7) 2.232.238)8) 0.0540.054

AnswersAnswers1)1) 4,2304,2302)2) 5,2205,2203)3) 15.115.14)4) 2.002.005)5) 0.01000.01006)6) 330.330.7)7) 2.222.228)8) 0.05420.0542

Write each of these to have three Write each of these to have three (3) sig figs. Round if you must.(3) sig figs. Round if you must.

ValueValue1)1) 4,2334,2332)2) 5,2205,2203)3) 15.10415.1044)4) 2.0052.0055)5) 0.0100.0106)6) 330.5330.57)7) 2.2252.2258)8) 0.054220.05422

AnswersAnswers1)1) 4,2304,2302)2) 5,2205,2203)3) 15.115.14)4) 2.002.00

Why not?Why not?1)1) 4,2004,2002)2) 5,220.5,220.3)3) 15.1015.10

MultiplicationMultiplication RememberRemember

• (factor(factor11) x (factor) x (factor22) x (factor) x (factornn) = product) = product

Answer (product) should have the Answer (product) should have the same number of sig figs as the least same number of sig figs as the least of the factors.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) (4 sig fig) x (2 sig fig) answer with 2 sig figs answer with 2 sig figs

37.448 37.448 37 37

Multiplication (cont’d)Multiplication (cont’d)

Answer (product) should have the Answer (product) should have the same number of sig figs as the least of same number of sig figs as the least of the factors.the factors.• Example:Example:

17.04 x 2.20 = 37.488 17.04 x 2.20 = 37.488 (from calculator)(from calculator)

(4 sig fig) x (3 sig fig) (4 sig fig) x (3 sig fig) answer with 3 sig figs answer with 3 sig figs

37.488 37.488 37.5 37.5

Only do your rounding in the FINAL STEP or Only do your rounding in the FINAL STEP or you could create rounding errors.you could create rounding errors.

DivisionDivision RememberRemember

• (dividend) ÷ (divisor) = quotient(dividend) ÷ (divisor) = quotient

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

75.5555 75.5555 76 76

Division (cont’d)Division (cont’d)

Answer (quotient) should have the Answer (quotient) should have the same number of sig figs as the lesser same number of sig figs as the lesser of the dividend or divisor.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) ÷÷ (3 sig fig) (3 sig fig) answer with 3 sig figs answer with 3 sig figs

75.5555 75.5555 75.6 75.6

Only do your rounding in the FINAL STEP or Only do your rounding in the FINAL STEP or you could create rounding errors.you could create rounding errors.

How many sig figs does How many sig figs does the answer have? the answer have?

10 x 2.5510 x 2.55 100 x 25100 x 25 100. x 25100. x 25 24.00 / 12.024.00 / 12.0 480 / 4480 / 4 22.44 / 14.222.44 / 14.2 (16 / 2) x 9(16 / 2) x 9

25.5 25.5 3030

2500 2500 20002000

2500 2500 25002500

ComputationsComputations

11

11

22

2 2 2.002.00

120 120 100100

1.580 28 1.580 28 1.581.58

72 72 7070

33

11

33

11

Put these numbers in Put these numbers in standard notationstandard notation

102.55 + 101.9102.55 + 101.9 100.0 + 91.22100.0 + 91.22 90 + 25.690 + 25.6

102.55 + 101.9102.55 + 101.9 14,400 + 49014,400 + 490 22.74 – 14.222.74 – 14.2 (16 / 2.0) + 9.0(16 / 2.0) + 9.0

204.45 204.45 204.4204.4

191.22 191.22 191.2191.2

115.6 115.6 120 120 or or

116 (116 (WhyWhy?)?)

ComputationsComputations

204.45 204.45 204.4204.4

14,890 14,890 14,90014,900

18.5418.54 18.518.5

8.0 + 9.08.0 + 9.0 17.017.0

Quiz TimeQuiz Time

Depending on the class’s behavior, Depending on the class’s behavior, it may be open-note or closed-note.it may be open-note or closed-note.

So So nownow you can stop asking you can stop asking “How many decimal places “How many decimal places

should I write?”should I write?”