Keith BatyWhitehouse High School

How close a measurement agrees with a true or accepted value.

How close several trials making the same measurement are to

each other. The reproducibility of data. Agreement among a set of

data.

Poor accuracy

Poor precision

Poor accuracy

Good precision

Good accuracy

Good precision

A metal bar about 9.8 inches long has been passed around to several groups of students. Each group is asked to measure the length of the bar. Each group has five students and each student independently measures the rod and records his or her result.

Which group has the most accurate measurement?

Student Group

Student 1

Student 2

Student 3

Student 4

Student 5

Group A 10.1 10.4 9.6 9.9 10.8

Group B 10.135 10.227 10.201 10.011 10.155

Group C 12.14 12.17 12.15 12.14 12.18

Group D 10.05 10.82 8.01 11.5 10.77

Group E 10 11 10 10 10

A metal bar about 9.8 inches long has been passed around to several groups of students. Each group is asked to measure the length of the bar. Each group has five students and each student independently measures the rod and records his or her result.

Which group has the most precise measurement?

Student Group

Student 1

Student 2

Student 3

Student 4

Student 5

Group A 10.1 10.4 9.6 9.9 10.8

Group B 10.135 10.227 10.201 10.011 10.155

Group C 12.14 12.17 12.15 12.14 12.18

Group D 10.05 10.82 8.01 11.5 10.77

Group E 10 11 10 10 10

Suppose a ruler is used to measure the length of an object as shown in the figure below.

Similarly, all measured quantities are generally reported in such a way that the last digit is uncertain. All digits in a measurement including the uncertain one are called significant figures.

Counting Significant Figures

• The following rules can be used to determine the number of significant figures (or digits).

• All non-zero digits are considered significant.

• If a zero is between two non-zero digits then it is significant.

• Leading zeros are never significant.

• Trailing zeros are only significant if there is a decimal present.

Examples

Measured Value

# of S. F.

2.456

1003.2

1.03000

0.0000402

230000

4

5

6

3

?

Exact numbers are considered to have an infinite number of significant figures. For example, if you said, “A is twice (or two times) as large as B”, the number 2 would be exact. Or, if you said “There are 4 quarts in a gallon”, the number 4 would be exact. Exact numbers usually involve counted values or definitions.

Multiplication and divisionFor multiplication and division, the number of

significant figures in the answer should be equal to the number of sig figs as the measurement with the least number of SIGNIFICANT FIGURES.

3.9 tooff round

89648.3

41.x

2783.2

Examples:3.40 x 4.5672 = 15.52848

3 5

round off to 15.5

(3 significant figures)

Addition and subtraction The result should be reported to the same number of decimal places as the least precise measurement (the measurement with the fewest decimal places).

6.95 tooff round

9463.6

20.2

423.1

3692.3

6.671 tooff round

6707.6

312.2

7793.8

Example: 2.487 + 330.4 + 22.59 = 355.477

round off to 355.5 (Uncertainty in tenths place)

 

 

 

 

 

 

 

 

9.   The following are placed in a beaker weighing 39.457 g: 2.689 g of NaCl, 1.26 g of sand and 5.0 g water . What is the final mass of the beaker? 10. If the beaker containing a sample of alcohol weighs 49.8767 g and the empty beaker weighs 49.214 g, what is the weight of the alcohol? 

meter (m)

liter (L)

gram (g)

deci (d) 10 dm = 1 m

centi (c) 100 cm = 1 m

milli (m) 1000 mm = 1 m

micro (μ) 106 μ m = 1 m

nano (n) 109 nm = 1 m

deka (da) 1 dam = 10 m

hecto (h) 1 hm = 100 m

kilo (k) 1 km = 1000 m

mega (M) 1 Mm = 106 m

English /Metric

1 in = 2.54 cm

1.06 qt = 1 L

1 lb = 454 g

CONVERSIOCONVERSION FACTORSN FACTORS

When I say I want to lose weight I should say I want to lose mass. I would weigh less on the moon. The problem is I would look the same in a mirror. I really want there to be less of me not less force of gravity on me

Mass a measure of the amount of matter

Weight a measure of the force of gravity on an object

Volume a measure of the amount of space an object occupies