Significant Figures

Physics

All nonzero digits are significant

1, 2, 3, 4, 5, 6, 7, 8, 9

Nonzero Digits

Embedded Zeros are Significant

Zeros between other nonzero digits are significant

60.5

3,008

340,506

Embedded Zeros

Leading Zeros are NOT significant

Zeros in front of nonzero digits are not significant

0.75

.0032

0.0005

Leading Zeros

Trailing Zeros in a number with a decimal place ARE significant

Zeros that are at the end of a number containing a decimal place ARE significant

5.0

33.20

4800.

Trailing Zeros

Trailing Zeros in a number without a decimal place are NOT significant

Zeros that are at the end of a number NOT containing a decimal place are NOT significant

50

3320

4800

Trailing Zeros II

a) 18.3 b) 183 c) .00183 d) 183.0

e) 50 f) 505 g) .0050 h) 5000.

i) 200.00 j) 0.00220 k) 22020

How many Sig-Figs ?

a) 18.3 3 b) 183 3 c) .00183 3 d) 183.0 4

e) 50 1 f) 505 3 g) .0050 2 h) 5000. 4

i) 200.00 5 j) 0.00220 3 k) 22020 4

How many Sig-Figs ?

The final answer should have the same number of decimal places as the number with the least number of decimal places.

90.3 + 2.23 = 92.53 = 92.5

180.1 + 5.202 + 3.32 = 188.632 = 188.6

Addition & Subtraction

The final answer has the same number of sig-figs as the number with the least number of sig-figs.

123 x 5.35 = 658.05 = 658

16 x 2 = 32 = 30

16 x 2.0 = 32 = 32

Multiplication & Division

20.23 + 17.405 + .230 = ________

20.12 + 5.2 + .245 +100.4 = ________

5.35 x 20.2 x 5.0 = _______

2.00 x 500 = _______

2.5 x 55.5 = ________

Express Result in Sig-Figs

20.23 + 17.405 + .230 = 37.865=37.86

20.12 + 5.2 + .245 +100.4 = 125.965=126.0

5.35 x 20.2 x 5.0 = 540.35 = 540

2.00 x 500 = 1000

2.5 x 55.5 = 138.75 = 140

Round Down whenever the digit following the last sig-fig is 0, 1, 2, 3 or 4

Examples of #’s with 3 sig-figs:

50.24 = 50.2

1.0038 = 1.00

230.29 = 230.

Round Down

Round Up whenever the digit following the last sig-fig is a 6, 7, 8 or 9

Examples of #’s with 3 sig-figs:

183.6 = 184

.053078 = .0531

23.46 = 23.5

Round Up

Round UP if the digit following the last sig-fig is a 5 followed by a nonzero digit.

Examples with 3 sig-figs:

23.451 = 23.5

.018752 = .0188

.102531 = .103

Rounding with 5’s I

Round DOWN if the last sig-fig is an even # and the next digit is a 5, with no other nonzero digits.

Round UP if the last sig-fig is an odd # and the next digit is a 5, with no other nonzero digits.

Examples of #’s with 3 sig-figs:

12.250 = 12.2

13.25 = 13.2

2.345 = 2.34

7.3850 = 7.38

Rounding with 5’s II

a) 12.35 b) 100.5 c) .0001055

d) 1.2251 e) 230,515 f) 456.5

g) 223.50 h) 1000.5

Express each in 3 Sig-Figs

a) 12.35 b) 100.5 c) .0001055

a) 12.4 b) 100. c) .000106

d) 1.2251 e) 230,515 f) 456.5

d) 1.23 e) 231,000 f) 456

g) 223.50 h) 1000.5

g) 224 h) 1000

Answers