1. Chapter 2 Measurement and Problem Solving

2. What is a Measurement? Quantitative observation.
Comparison to an agreed upon standard.
Every measurement has a number and a unit.

3. Scientific Notation
Technique used to express very large or very small numbers.
The sun’s
diameter is
1,392,000,000 m.
An atom’s
average diameter is m.

4. Scientific Notation
Expresses a number as a product of a number between 1 and 10 and the appropriate power of 10.
The sun’s
diameter is
1.392 x 109 m.
An atom’s
average diameter is
3 x m.

5. Scientific Notation
The number of places the decimal point is moved determines the power of 10. The direction of the move determines whether the power of 10 is positive or negative.

6. Scientific Notation
If the decimal point is moved to the left, the power of 10 is positive.
Sun’s diameter = 1,392,000,000 m = x 109 m.
If the decimal point is moved to the right, the power of 10 is negative.
Average atom’s diameter = m =
3 x m.

7. Scientific Notation
The World’s population is estimated to be 7,187,000,000 people. Express this number in scientific notation.
Express the following numbers in scientific notation: ; 72.
Express the following numbers in standard notation: x 10-7; 9.5 x 104.

8. Significant Figures Writing numbers to reflect precision.
All measurements have some degree of uncertainty.

9. Significant Figures

10. Significant Figures
When writing measurements, all the digits written are known with certainty except the last one, which is an estimate.
Record the certain digits and the first uncertain digit (the estimated number).
45.872
Certain
Estimated

11. Significant Figures All non-zero digits are significant.
1.5 has 2 significant figures.
Interior zeros are significant.
1.05 has 3 significant figures.
Trailing zeros after a decimal point are significant.
1.050 has 4 significant figures.

12. Significant Figures Leading zeros are NOT significant.
has 4 significant figures.
Zeros at the end of a number without a written decimal point are ambiguous.
150 has 2 or 3 significant figures—ambiguous.

13. Significant Figures
A number whose value is known with complete certainty is exact.
Exact numbers have an unlimited number of significant figures.

14. Significant Figures in Calculations
When multiplying or dividing measurements with significant figures, the result has the same number of significant figures as the measurement with the fewest number of significant figures.
× × = = 45
÷ = =

15. Significant Figures in Calculations
When rounding to the correct number of significant figures, if the number after the place of the last significant figure is:
0 to 4, round down.
5 to 9, round up.
In a series of calculations, carry the extra digits through to the final result and then round off.

16. Significant Figures in Calculations
When adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the fewest number of decimal places.
= = 9.21
= = 0.8

17. Significant Figures in Calculations
An impossibly regular, paved walkway mysteriously appears overnight; leading out of Seattle. Careful measurement shows this walkway to be 15,432 meters long and 0.42 meters wide. To the correct number of significant figures, what area is covered by walkway? How would this number change if the walkway were 0.41 meters wide? meters wide?
By the next morning, this walkway has grown 0.42 meters. To the correct number of significant figures, how long is it now?

18. Units of Measurement
Units tell the standard quantity to which we are comparing the measured property.
Scientists use a set of standard units for comparing all our measurements.

19. Units of Measurement The SI System Quantity Unit Symbol Length meter m
Mass
kilogram kg
Time
second s
Temperature
kelvin K

20. Units of Measurement Length
Measure of the two-dimensional distance an object covers.

21. Units of Measurement Mass
Measure of the amount of matter present in an object.
Weight: measure of the gravitational pull on an object.

22. Units of Measurement
All units in the SI system are related to the standard unit by a power of 10.
The power of 10 is indicated by a prefix.

23. Units of Measurement Prefix Symbol Decimal Equivalent Power of 10
mega- M
1,000,000
Base x 106
kilo- k
1,000
Base x 103
deci- d
0.1
Base x 10-1
centi- c
0.01
Base x 10-2
milli- m
0.001
Base x 10-3
micro-
Base x 10-6
nano- n
Base x 10-9

24. Units of Measurement Volume
Measure of the amount of 3-D space occupied by a substance—a derived unit.

25. Unit Conversions
Dimensional analysis: using units as a guide to problem solving.
A quantity in one unit is converted to an equivalent quantity in a different unit by using a conversion factor that expresses the relationship between units.

26. Unit Conversions
A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? How many centimeters?
What is the volume of a 1.25 gallon jug in cubic centimeters? Cubic inches?
(1 gal = 4 qts; 1 L = qts)

27. Density
Mass of substance per unit volume of the substance.

28. Density Volume vs. Mass of Brass y = 8.38x Mass, g Volume, cm3 20 4020 40 60 80
100
120
140
160
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
Volume, cm3
Mass, g

29. Density
Volume of a solid can be determined by water displacement.

30. Density
Density : solids > liquids > gases

31. Density
A certain mineral has a mass of 17.8 g and a volume of 2.35 cm3. What is the density of this mineral?
What is the mass of a 49.6 mL sample of a liquid, which has a density of 0.85 g/mL?
Copper has a density of 8.96 g/cm3. If 75.0 g of copper is added to 50.0 mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise?

32. Density

33. Summary of Topics: Chapter 2
Scientific notation
Significant figures
Exact numbers, Measured numbers
Metric units, prefixes
Difference between mass and weight
Conversion factors
Density; D = m/v