1. Math and Measurement
Review

2. Chemistry is the science of substances ― their structure,
their properties, and the reactions that change them into
other substances.
Linus Pauling, “General Chemistry”

3. 1 ≤ |a| < 10, n is an integer
Scientific/Exponential Notation
a x 10n
1 ≤ |a| < 10, n is an integer
Negative exponent:

4. Express the following numbers in scientific notation25
2500
−270000
0.25 −
Read Appendix I: A

5. Never drop units! Examples that involve unit calculations
Units are involved in calculations just as numbers.
Never drop units!
Your calculator does not deal with units.
You must work on it!

6. a x 5 m A physical quantity can be considered as
a product of a number and its unit.
a x
number
unit
5 m

7. C A B a x − b x = (a − b) x AB = 15 m AC = 10 m CB = ?
CB = AB − AC = 15 m − 10 m
= (15 − 10) m
= 5 m

8. H = 3 cm W = 6 cm Area = W x H = 6 cm x 3 cm = 18 cm2
a x • b x = ab x2
H = 3 cm
W = 6 cm
Area = W x H = 6 cm x 3 cm = 18 cm2

9. (a x)3 = a3 x3
What is the volume of a cube with edge
length 5 cm?
V = L3 = (5 cm)3 = 53 (cm)3 = 125 cm3

10. A B
15 m C
10 m D
How many times is AB compared to CD in length?

11. A B 15 m Time consumed to move from A to B is 5 s.
What is the average speed?
meters per second

12. Chem 1211 and 1212

13. Mass is a measure of the amount of material in an
object.
Unit: kg
Weight is the force that gravity exerts on an object.
F = ma
Unit: N
G = mg
Mass ≠ Weight

14. Chemistry is a discipline of science that strongly
depends on experiments.
Experiments  Measurements
Some basic concepts related to measurements

15. Reliability of Measurements
Accuracy refers to the agreement of a particular
measurement with the true value.

16. experimental value (m)
To quantify accuracy, define:
absolute error = experimental value − true value
True value = 50 m
experimental value (m)
absolute error (m) 52 2 50 51 1 48 −2
sign of error: direction
|error|: size

17. relative error = absolute error / true value
unknown
relative error = absolute error / true value
= absolute error / theoretical
relative error is often given in percentage:
| |: to make % error a positive number

18. experimental value (m)
True value = 50 m
experimental value (m)
absolute error (m) 52 2 50 51 1 48 −2
What are the percent errors for the measurements
listed in the table?

19. Based on source Random Error: random, cannot avoid. But
can take average of multiple measurements
to reduce to certain degree.
Systematic Error: same direction, could fix

20. true value
Random error only

21. Random error and systematic error.
true value
Random error and systematic error.

22. Reliability of Measurements
Accuracy refers to the agreement of a particular
measurement with the true value.
Precision is the degree of agreement among several
measurements.
Accuracy ≠ Precision

23. The Results of Several Dart Throws Show the Difference Between Precise and Accurate

24. How to report a measurement?

25. mL

26. We report a measurement by recording
ALL the certain digits + ONE uncertain digit
Significant Figures
(except leading zeros)

27. Chapter 1, Unnumbered Figure 2, Page 14

28. Or conversions involving prefixes:

29. 1 ≤ |a| < 10, n is an integer
Note: Scientific expression does not change the number of sig figs.
a x 10n
1 ≤ |a| < 10, n is an integer
Only need to count sig figs in “a”

30. Conversion factor
= 1
#: copy from the relation between two units.

31. Physical quantity with given unit x Conversion factor
= Physical quantity with desired unit
5.0 in = ? cm
3.2 m = ? mm
5.000 in = ? cm
3.2 cm = ? mm
5.000 in = ? m
6.81 cm2 = ? in2
19.21 cm = ? in
66 km/h = ? m/s
7.8 g/cm3 = ? kg/m3

32. Three Basic Physical Quantities
Volume
Density
Temperature

33. Volume and its units 1 m = 10 dm = 100 cm
How much room an object occupies
in space.
1 m = 10 dm = 100 cm
(1 m)3 = (10 dm)3 = (100 cm)3
1 m3 = 103 dm3 = 106 cm3
For liquid, define: 1 L = 1 dm3
Then: 1 mL = ? cm3
= 1 cm3

34. Density: mass of a substance per unit volume of the substance.
Unit: kg/m3, g/cm3, g/mL
Density is a property of substances. It is determined by the
substance’s identity and external conditions, not by the
substance’s mass or volume.

36. How to find density?
How to find mass?
balance
How to find volume?
• Liquid: graduated cylinder, beaker, buret, pipet…
• Solid
Regular shape: Measure dimensions,
then calculate
Irregular shape: water displacement

37. TK, Kelvin scale, K (not °K)
Temperature: a measure of hotness or coldness of an object.
Temperature scales
TC, Celsius scale, °C
TF, Fahrenheit scale, °F
TK, Kelvin scale, K (not °K)

38. Temperature conversions
Normal body temperature is 98.6 °F. Convert this temperature to
the Celsius and Kelvin scales.