1. Chapter 2
Measurements and
Calculations

2. Scientific Notation
Technique used to express very large or very small numbers: for example, 2,009,345,234 or
Expressed as a product of a number between 1 and 10 and a power of 10 3

3. Writing Numbers in Scientific Notation
Locate the decimal point.
Count the number of places the decimal point must be moved to obtain a number between 1 and 10.
Multiply the new number by 10n where n is the number of places you moved the decimal point.
Determine the sign on the exponent n.
If the decimal point was moved left, n is +
If the decimal point was moved right, n is –
If the decimal point was not moved, n is 0 4

4. Write the following numbers in scientific notation:
2,009,345,234 B

5. Converting from Scientific Notation to Standard Form
Determine the sign of n in 10n
If n is + the decimal point will move to the right.
If n is – the decimal point will move to the left.
Determine the value of the exponent of 10.
Tells the number of places to move the decimal point
Move the decimal point and rewrite the number. 5

6. Convert from Scientific Notation to Standard Form:
x 105
x 10-4

7. Related Units in the Metric System
All units in the metric system are related to the fundamental unit by a power of 10.
A power of 10 is indicated by a prefix.
Prefixes are always the same, regardless of the fundamental unit.
Examples:
kilogram = 1000 grams
kilometer = 1000 meters 6

8. Some Fundamental SI Units

9. Prefixes
All units in the metric system utilize the same prefixes

10. Length 7

11. Volume Measure of the amount of 3-D space occupied by a substance
SI unit = cubic meter (m3)
Commonly measure solid volume in cubic centimeters (cm3)
1 mL = 1 cm3 8

12. Mass Measure of the amount of matter present in an object
SI unit = kilogram (kg)
1 kg = pounds, 1 lb = g
68 kg = 150 lbs
Commonly measure mass in grams (g) or milligrams (mg) 9

13. Uncertainty in Measured Numbers
A measurement always has some amount of uncertainty.
To understand how reliable a measurement is, we must understand the limitations of the measurement.
Example: 10

14. Reporting Measurements
Significant figures: system used by scientists to indicate the uncertainty of a single measurement
Last digit written in a measurement is the number that is considered uncertain
Unless stated otherwise, uncertainty in the last digit is ±1. 11

15. Rules for Counting Significant Figures
Nonzero integers are always significant.
example: = 4 sig figs
Zeros
Leading zeros never count as significant figures.
example: = 3 sig figs
Captive zeros are always significant.
example: = 5 sig figs
Trailing zeros are significant if the number has a decimal point.
example: = 4 sig figs 12

16. Exact Numbers Exact numbers: numbers known with certainty
Counting numbers
number of sides on a square
Defined numbers
100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm
1 minute = 60 seconds
Have unlimited number of significant figures 14

17. Rules for Rounding Off If the digit to be removed:
is less than 5, the preceding digit stays the same.
example:
is equal to or greater than 5, the preceding digit is increased by 1.
In a series of calculations, carry the extra digits to the final result, then round off.
When rounding off use only the first number to the right of the last significant figure. 13

18. Round these numbers to four significant figures:
443,678
80, 332
7.8097

19. Multiplication/Division with Significant Figures
Result must have the same number of significant figures as the measurement with the smallest number of significant figures:
example: 3.5 x =
example: 4.98/11.76 = 16

20. Adding/Subtracting Numbers with Significant Figures
Result is limited by the number with the smallest number of significant decimal places
example: 17

21. Problem Solving and Dimensional Analysis
Many problems in chemistry involve using equivalence statements to convert one unit of measurement to another.
Conversion factors are generated from equivalence statements.
e.g. 1 mi = 5,280. ft can give:
1 mi/5280. ft or
5280. ft/1 mi 18

22. Converting One Unit to Another
Find the relationship(s) between starting and goal units. Write equivalence statement for each relationship.
Given quantity x unit factor = desired quantity
Write a conversion factor for each equivalence statement.
Arrange the conversion factor(s) to cancel with starting unit and result in goal unit. 20

23. Converting One Unit to Another (cont.)
Check that units cancel properly.
Multiply and divide the numbers to give the answer with the proper unit.
Check significant figures.
Check that your answer makes sense! 21

24. Convert the following: (Use Table 2.7)
180 lbs to kg
12.3 mi to in.

25. Temperature Scales 22

26. Some facts concerning the temperature scales:
The size of each degree is the same for the Celsius and Kelvin scales.
The Fahrenheit degree is smaller than the Celsius and Kelvin unit.
F – 180 degrees between freezing and boiling point of water
C – 100 degrees between freezing and boiling point of water
All three scales have different zero points.

27. Converting between Kelvin and Celsius Scales ToC + 273 = K
Celsius to Kelvin: add 273 to C temperature
example: Convert 46o C to K
Kelvin to Celsius: subtract 273 from K temperature
example: Convert 4 K to C

28. Converting from Celsius to Fahrenheit
Requires two adjustments:
1. Different size units; 180 F degrees = 100 C degrees
2. Different zero points
ToF = 1.80(ToC) + 32
Convert 30oC to oF

29. Converting from Fahrenheit to Celsius
ToC = (ToF – 32)/1.80
Convert 102oF to oC

30. Density
Volume of a solid can be determined by water displacement. 23

31. Using Density in Calculations24

32. Using Density in Calculations
Calculate the density of an object which weighs 35.7 g and occupies a volume of 21.5 mL.
Calculate the mass of a piece of copper which occupies
2.86 cm3. (density = 8.96 g/cm3)
Calculate the volume of an object with a density of 4.78 g/mL
and mass of 20.6 grams.