1. Solve Apply the concepts to this problem.
Sample Problem 3.5
Solve Apply the concepts to this problem.
Align the decimal points and add the numbers.
a meters
meters
meters
meters 2

2. Solve Apply the concepts to this problem.
Sample Problem 3.5
Solve Apply the concepts to this problem.
a meters
meters
meters
meters 2
369.8 meters = x 102

3. Solve Apply the concepts to this problem.
Sample Problem 3.5
Solve Apply the concepts to this problem.
Align the decimal points and subtract the numbers.
b meters
meters
meters 2

4. Solve Apply the concepts to this problem.
Sample Problem 3.5
Solve Apply the concepts to this problem.
b meters
meters
meters 2
= meters
= x 101 meters

5. Multiplication and Division
Significant Figures in Calculations
Multiplication and Division
In calculations involving multiplication and division, you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures.
The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements.

6. Significant Figures in Multiplication and Division
Sample Problem 3.6
Significant Figures in Multiplication and Division
a meters x 0.34 meter
b meters x 0.70 meter
c meters2 ÷ 8.4 meters
d meter2 ÷ meter

7. Answers
a meters x 0.34 meter = meters2 = 2.6 meters2 b meters x 0.70 meter = 1.47 meters2 = 1.5 meters2 c meters2 ÷ 8.4 meters = meter = 0.29 meter d meters2 ÷ meter = meters = 18.3 meters

8. In what case are zeros not significant in a measured value?

9. In what case are zeros not significant in a measured value?
Sometimes zeros are not significant when they serve as placeholders to show the magnitude of the measurement.

10. Key Concepts
In scientific notation, the coefficient is always a number greater than or equal to one and less than ten. The exponent is an integer.
To evaluate accuracy, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

11. Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation.

12. Key Equations Error = experimental value – accepted value
Percent error =
|error |
____________

13. Glossary Terms
measurement: a quantitative description that includes both a number and a unit
scientific notation: an expression of numbers in the form m x 10n, where m is equal to or greater than 1 and less than 10, and n is an integer
accuracy: the closeness of a measurement to the true value of what is being measured
precision: describes the closeness, or reproducibility, of a set of measurements taken under the same conditions

14. Glossary Terms
accepted value: a quantity used by general agreement of the scientific community
experimental value: a quantitative value measured during an experiment
error: the difference between the accepted value and the experimental value
percent error: the percent that a measured value differs from the accepted value
significant figure: all the digits that can be known precisely in a measurement, plus a last estimated digit

15. BIG IDEA
Scientists express the degree of uncertainty in their measurements and calculations by using significant figures.
In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.

16. MEASUREMENT

17. SI Units of Measurement
SI Base Units
Quantity
SI base unit
Symbol
Length
meter m
Mass
kilogram kg
Temperature
kelvin K
Time
second s
Amount of substance
mole
mol
Luminous intensity
candela cd
Electric current
ampere A

18. Commonly Used Metric Prefixes
Symbol
Meaning
Factor
mega M
1 million times larger than the unit it precedes
106
kilo k
1000 times larger than the unit it precedes
103
deci d
10 times smaller than the unit it precedes
10-1
centi c
100 times smaller than the unit it precedes
10-2
milli m
1000 times smaller than the unit it precedes
10-3
micro μ
1 million times smaller than the unit it precedes
10-6
nano n
1 billion times smaller than the unit it precedes
10-9
pico p
1 trillion times smaller than the unit it precedes
10-12

19. Metric Units of Mass Unit Symbol Relationship Example
Kilogram (base unit) kg
1 kg = 103 g
small textbook ≈ 1 kg
Gram g
1 g = 10-3 kg
dollar bill ≈ 1 g
Milligram mg
103 mg = 1 g
ten grains of salt ≈ 1 mg
Microgram μg
106 μg = 1 g
particle of baking powder ≈ 1 μg

20. Volume Metric Units of Volume Unit Symbol Relationship Example Liter L
base unit
quart of milk ≈ 1 L
Milliliter mL
103 mL = 1 L
20 drops of water ≈ 1 mL
Cubic centimeter
cm3
1 cm3 = 1 mL
cube of sugar ≈ 1 cm3
Microliter μL
103 μL = 1 L
crystal of table salt ≈ 1 μL

21. Temperature Conversions
K = °C + 273
°C = K – 273

22. Density
The relationship between an object’s mass and its volume tells you whether it will float or sink.
This relationship is called density.
Density is the ratio of the mass of an object to its volume.
mass
volume
Density =

23. Density
When mass is measured in grams, and volume in cubic centimeters, density has units of grams per cubic centimeter (g/cm3).
The SI unit of density is kilograms per cubic meter (kg/m3).
Density is an intensive property

24. Density
This figure compares the density of four substances: lithium, water, aluminum, and lead.
Increasing density (mass per unit volume)
10 g
0.53 g/cm3
19 cm3
10 cm3
3.7 cm3
0.88 cm3
1.0 g/cm3
2.7 g/cm3
0.88 g/cm3

25. Density
Because of differences in density, liquids separate into layers.
As shown at right, corn oil floats on top of water because it is less dense.
Corn syrup sinks below water because it is more dense.
Corn oil
Water
Corn syrup