1. Chapter 2: Measurements and Calculations

2. Units of Measurement
A standard system for measurements called Le Systeme Internatitional d’Unites was adopted by the General Conference on Weights and Measures in 1960.
These units of measurements are abbreviated SI units.

3. Units of Measurement
Table 2-1 on page 34 of your text lists the 7 base SI units.
Quantity Unit Name Abbreviation
Length meter m
Mass kilogram kg
Time second s
Temperature Kelvin K
Amount of Mole mol
Substance

4. SI Prefixes (P35) Prefix- Symbol Exponent Factor Value Tera T 1012
Giga G
109
Mega M
106
Kilo k
103
1000
Hecto h
102
100
Deka da
101 10
Deci d
10-1
0.1
Centi c
10--2
0.01
Milli m
10-3
0.001
Micro μ
10-6
Nano n
10-9

5. Units of Measurement Page 36
The base SI units may be combined to form derived units.
For example volume has three dimensions. Therefore volume can be expressed as
m x m x m = m3
Table 2-2 on page 35 of your text lists the SI prefixes. Please review these.

6. Unit Conversions
A conversion factor is a ratio derived from the equality between two different units of measurement and can be used to convert from one unit to another unit.
For example 1 m = 1000 mm
So the ratio and
equal 1, and

7. Unit Conversions Your Turn:
If you have 350 mg, how many grams do you have?
Table 2-2 on page 35 of your text lists the SI prefixes.

8. DENSITY is an important and useful physical property
Water
Mercury
Gold
13.6 g/cm3
19.3 g/cm3
1.0 g/cm3

9. Water Water is used as one of the bases for the SI unit system.
The density of water is set to 1.0 g/cm3, in other words, 1 cm3 of water weighs 1 g. Also 1 mL is equivalent to 1 cm3.
Therefore 1 g = 1 cm3 = 1 mL

10. Problem: A piece of copper has a mass of 57. 54 g. It is 9
Problem: A piece of copper has a mass of g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. Calculate its density (g/cm3).

11. SOLUTION
1. Get dimensions in common units. . 95
mm • 1 cm 10 mm =
095

12. SOLUTION
1. Get dimensions in common units.
2. Calculate volume in cubic centimeters.
(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm3
3. Calculate the density. . 95
mm • 1 cm 10 mm =
095 57 . 54 g = . 3 9 g / cm 3 6 . 4 cm

13. Your Turn: Mercury (Hg) has a density of 13. 6 g/cm3
Your Turn: Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 mL of Hg in grams?
Solve the problem using DIMENSIONAL
ANALYSIS.
Recall that cm3 = mL

14. First, recall that 1 cm3 = 1 mL
PROBLEM: Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 mL of Hg?
First, recall that 1 cm3 = 1 mL
95 ml = 95 cm3
Then, use dimensional analysis to calculate mass.

15. Practice
What is the volume of a sample of liquid mercury that has a mass of 76.2 g given that the density of mercury is 13.6 g/mL?

16. Precision and Accuracy
Precision is a measure of how nearly duplicate measurements agree with each other.
Accuracy is a measure of how near a measurement is to the true value.

17. Percent Error
Percent error is the relative difference between a measurement and the true value reported as a percentage.
Percent error is calculated

18. Percent Error For example
You obtain the value 5.55 g upon weighing a beaker full of water. The actual weight of the beaker full of water is 5.75 g. What is the percent error of you measurement?
= %

19. Significant Figures All nonzero digits are significant.
All zeros that lie between nonzero digits are significant.
None of the zeros that lie to the left, or in front, of the first nonzero digit are significant.
Zeros to the right of the last nonzero digit are significant ONLY if they lie to the right of the decimal point.

20. Significant Figures
For example how many significant figures are in each of the following numbers
Number Significant Digits

21. Significant Figures Adding and Subtracting
When adding and subtracting, line up the decimal points and round all numbers down to the one with the fewest decimal digits.
For example
Position of the
least sig. fig.
hundreds tenths
tenths
hundreds

22. Significant Figures Multiplying and Dividing
Regardless of the locations of decimal points, the result must have no more significant digits than those in the factor with the smallest number of significant digits.
For example
4.0 x 3.00 x 2.0 = 24
2 x = 6

23. Scientific Notation
Scientific notation is used to express very large or very small numbers.
In scientific notation in the form M x 10n, where the factor M is a number equal to or greater than 1 and less and 10, and n is a whole number.
For example
101,000 = 1.01 x 105, and
= 4.0 x 106

24. Direct Proportions
Two quantities are directly proportional to each other if dividing one by the other gives a constant value.
This can be expressed mathematically as
y/x = k, or y = kx
Does the equation y = kx look familiar?

25. Inverse Proportions
Two quantities are inversely proportional to each other if multiplying one by the other gives a constant value.
This can be expressed mathematically as
yx = k, or y = k/x