1. Measurements and Calculations
Chapter 2
Measurements and Calculations

2. Measurements Numbers Must consist a number and units E.g
Quantitative observations
Must consist a number and units
E.g

3. 2.1 Scientific Notation
To show how very large or very small numbers can be expressed as the product of a number between 1 and 10 and a power of 10
Negative power = small value
Moving the decimal point to the right
=> 3.5 x 10-5
Positive power = large value
Moving the decimal point to the left
3568 = x 103

4. 2.1 Scientific Notation
Express the following numbers in scientific notation
238,000
1,500,000
0.104

5. 2.2 Units Part of measurement Unit system Require common units
English system
Metric system or International system (SI)

6. Table 2.1 Some Fundamental SI units
Physical Quantity
Name of unit
Abbreviation
Mass
kilogram kg
Length
meter m
Time
second s
temperature
Kelvin K

7. Table 2.2 The Common Used Prefixes in the Metric System
Symbol
Meaning
Scientific Notation
mega M
1,000,000
106
kilo k
1,000
103
deci d
0.1
10-1
centi c
0.01
10-2
milli m
0.001
10-3
micro
10-6
nano n
10-9

8. 2.3 Measurements of Length, Volume and Mass
meter
Volume
cm3 or ml
Mass kg
Weigh

9. 2.3 Measurements of Length, Volume and Mass
Consider the following objects then provide an appropriate measurement to each object
2.0 L
45.0 g
200 km
42.0 cm3

10. 2.4 Uncertainty in Measurement
Person
Result of Measurement 1
2.85 cm 2
2.84 cm 3
2.86 cm 4 5

11. 2.4 Uncertainty Every measurement has some degree of uncertainty
The first digit is the certain digit
The last digit in the measurement is the uncertain digit
Determined by “guessing”

12. 2.4 Uncertainty
Determine the uncertain digit (estimate digit) in the following examples
2.54
60.028
1500
0.0078

13. 2.5 Significant Figures Rules Nonzero integers are always significant
1, 2, 3 ……
Leading zeros are never significant
=> 2 s.f
Captive zeros are always significant
103 => 3 s.f
Trailing zeros at the right end of number are significant
2.30 => 3 s.f
Exact number or counting number are never significant
2 books => none or indefinite

14. 2.5 Significant Figures
Determine the significant figures in each of the following measurements
A sample of an orange contains g of vitamin C
A forensic chemist in a crime lab weighs a single hair and records its mass as g
The volume of soda remaining in a can after a spill is L
There are 30 students enrolled in the class

15. Activity (2.1 -2.4) What is the SI unit for time?
What is the prefix for k? What does it mean?
When do you use cm3?
What is the difference between mass and weigh?

16. Activity ( )
Determine the significant figures and the uncertain digit in the following measurements:
2.56 cm
10.3 g
0.006 L
15 roses lb

17. 2.5 Round Off Numbers Rules for Rounding Off
If the digit to be removed
is less than 5, the preceding digit stays the same
3.13 (3 s.f) => 3.1 (2 s.f)
is equal to or greater than 5, the preceding digit is increased by 1
6.35 (3 s.f) => 6.4
6.36 (3 s.f) => 6.4
In a series of calculations, carry the extra digits through to the final result and then round off

18. 2.5 – Determining Significant Figures in Calculation
Multiplication and Division
Report answer with the least number of significant figures
E.g x 1.4 = = 6.4
8.315 ÷ 298. = =
Addition and Subtraction
Report answer with the least number of decimal places
E.g = = 30.1
0.678 – 0.1 = = 0.6

19. Examples
Without performing the calculations, tell how many significant figures each answer should contain =
1081 – 7.25 =
2.3 x 3.14 =
The total cost of 3 boxes of candy at $2.50 a box

20. Examples
Carry out the following mathematical operations and give each result to the correct number of significant figures
5.18 x =
116.8 – 0.33 =
(3.60 x 10-3) x (8.123) ÷ 4.3 =
(1.33 x 2.8) =

21. 2.6 Problem Solving and Dimensional Analysis
Also known as unit factor or factor-label method
First, determined the units of the answer
Second, multiply (or divide) conversion factor so that units are not need in the answer are cancelled out and units needed in the answer appear appropriately in either the numerator or denominator of the answer.
Check for correct significant figures
Ask whether your answer makes sense

22. Equality and Conversion Factors
Equality = equivalent
(English metric to English-English)
2.54 cm = 1 in
1 m = yd
1 kg = lb
453.6 g = 1lb
1L = 1.06 qt
1ft3 = L
Conversion Factor

23. Conversion Factors: One Step Problems
An Italian bicycle has its frame size given as 62 cm. What is the frame size in inches?
A new baby weighs 7.8 lb. What is its mass in kilograms?
A bottle of soda contain 2.0 L. What is its volume in quarts?

24. Conversion Factors: Multiple – Step Problems
The length of the marathon race is approximate 26.2 mi. What is this distance in kilometer?
How many seconds in one day?
You car has a 5.00-L engine. What is the size of this engine in cubic inches?

25. Freezing Point / Boiling

26. Boiling Point

27. 2.7 Temperature Conversion
Celsius to Kelvin
TK = ToC + 273
Kelvin to Celsius
ToC = TK -273
Celsius to Fahrenheit
ToF = 1.80 (ToC) + 32
Fahrenheit to Kelvin
ToC = ToF - 32
1.80

28. Example
If your body temperature is 312 K, what is it on the Celsius scale?
You’re traveling in a metric county and get sick. You temperature is 39oC. What is it on the Fahrenheit scale?
Pork is considered to be well done when its internal temperature reaches 160.oF. What is it on the Celsius scale?

29. 2.8 Density
Defined as the amount of matter present in a given volume of substance.
If each ball has the same mass, which box would weigh more? Why?

30. Examples
A block has a volume of 25.3 cm3. Its mass is 21.7g . Calculate the density of the block.
A student fills a graduated cylinder to 25.0 mL with liquid. She then immerse a solid in the liquid. The volume of the liquid rises to 33.9 ml. The mass of the solid is 63.5g. What is its density?

31. Examples
Isopropyl alcohol has a density of g/ml. What volume should be measured to obtain 20.0 g of liquid?
A beaker contains 725 mL of water. The density of water is 1.00 g/mL. Calculate the volume of water in liters. Find the mass of the water in ounces.