1. Math Tool Kit for Chemistry

2. Goals and Objectives What is the correct way to take a measurement?
What are significant figures in a measurement?
How do we count SFs in a measurement?
How do we use SFs in a calculation?
How do we round off answers correctly?
How is scientific notation used?
What is a percent error calculation?
What units of measurement do scientists use around the world?
How do we convert units of measurement?

3. Reliable Measurements
ACCURATE: close to the true value
PRECISE: close to each other, repeatable
RECORDED CORRECTLY: have one estimated digit
When used in calculations they are rounded correctly!

4. All measurements should have ONE estimated digit between the markings

5. You Try 

6. 1.36 cm

7. You Try 

8. 1.25 cm
2.2 cm

9. You Try 

11. Uncertainty in measurements
Different scales and different estimations result in UNCERTAINTY in all measurements.

12. You Try 

13. 21.5 mL

14. Measuring Mass Our balances have FOUR beams.
They are very precise and require your patience and skill!
The last beam is read to 3 decimals.

17. g

18. https://youtu.be/XTHTBvXFZns

19. Counting SFs

20. NEVER SIGNIFICANT
ALWAYS SIGNIFICANT
Leading zeroes
Trailing zeroes IF THERE IS NO DECIMAL IN THE MEASUREMENT
Non-zero numbers
Captive zeroes
Trailing zeroes IF THERE IS A DECIMAL IN THE MEASUREMENT

21. This measurement has 10 SFs!

22. You Try 
SFs
SFs
SFs

23. Significant Figures - You Try 
Examples: How many significant figures?
99,000
2 sig figs
99,000.
5 sig figs
0.0099
2 sig figs
0.0990
3 sig figs

24. Trick for counting SFs

25. Counting Significant Figures
The Atlantic – Pacific Rule:
Pacific (Present):
If decimal point is present, start with the first non-zero number on the left.
Atlantic (Absent):
If decimal point is absent, start with the first non-zero number on the right.

27. You Try 
10.2
103
103.0
200
5,269,000
10.036
0.258

28. You Try 
10.2
103
103.0
200
5,269,000
10.036
0.258 3 4 1 6 5

29. Calculating with Significant Figures (+/-)
When you use your measurements in calculations, your answer may only be as exact as your least exact measurement.
For addition and subtraction, round to the fewest decimal places.
Example: (3 decimals) (1 decimal) (unrounded) (rounded) =
67.7
Example: (3 decimals) (2 decimals) (unrounded) (rounded) =
22.35

30. Calculating with Significant Figures (+/-)
For addition and subtraction, round to the fewest decimal places
Watch out for these…..
Example: (2 decimals) (2 decimals) (unrounded) (rounded) =
9.00
Example: (0 decimals) (3 decimals) (unrounded) (rounded) =
101

31. Practice Rounding Your Answers
Examples: Round each to TWO decimals
Br =
79.90
N =
14.01
Kr =
83.80
Ag =
107.87

32. Calculating with Significant Figures (x/÷)
When you use your measurements in calculations, your answer may only be as exact as your least exact measurement.
For multiplication and division, round to the fewest significant figures.
Example: (5 SFs) (3 SFs) (unrounded) (rounded)
m x m = m2
875 m2
Example: (3 SFs) (1 SF) (unrounded) (rounded)
0.365 m3 ÷ m = m2
20 m2

33. Calculating with Significant Figures (x/÷)
When you use your measurements in calculations, your answer may only be as exact as your least exact measurement.
For multiplication and division, round to the fewest significant figures.
Example: (3 sigfigs) (1 sigfig) (unrounded) (rounded)
x = 3

34. Practice Rounding Your Answers
Examples: Round each to 3SFs
40.06
40.1
0.174
0.2006
0.201

37. Scientific Notation
A shorthand system of writing very large or very small numbers.
The power of 10 (the exponent), is the number of times the decimal point is moved.
The coefficient must be between 1 and 10.

41. Scientific Notation - You Try 
Examples: What would each of these numbers be in scientific notation?
NOTE: Retain the same SFs!!!
3000
3 x 103
32,000
3.2 x 104
0.05
5 x 10-2
0.0058
5.8 x 10-3

42. Scientific Notation & Significant Figures - You Try 
Always retain the same SFs when changing from scientific notation ⟷ standard notation
99,000
2 SFs = 9.9 x 10 4
99,000.
5 SFs = x 10 4
0.0099
2 SFs = 9.9 x 10 -3
0.0990
3 SFs = 9.90 x 10 -2

43. SFs, Rounding, SN Examples: Round as indicated and answer in SN 99,000
3 SFs & SN
9.90 x 104
0.0099
1 SF & SN
1 x 10-3

44. Percent Error Calculations
% ERROR = |𝑴𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝑽𝒂𝒍𝒖𝒆 −𝑻𝒓𝒖𝒆 𝑽𝒂𝒍𝒖𝒆| 𝑻𝒓𝒖𝒆 𝑽𝒂𝒍𝒖𝒆 x 100
Example: A student measures a mass of 3.697g and the true value is g. What is the percent error in the measurement?
𝟑.𝟔𝟗𝟕 −𝟒.𝟏𝟓𝟓 𝟒.𝟏𝟓𝟓 x 100 = 𝟎.𝟒𝟓𝟖 𝟒.𝟏𝟓𝟓 x 100 = 11.0% (3SF)
ALWAYS SHOW ALL THREE STEPS IN YOUR WORK!

45. You Try  % ERROR = |𝑴𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝑽𝒂𝒍𝒖𝒆 −𝑻𝒓𝒖𝒆 𝑽𝒂𝒍𝒖𝒆| 𝑻𝒓𝒖𝒆 𝑽𝒂𝒍𝒖𝒆 x 100
What is the % error for a volume measurement of 4.26mL if the accepted value is 4.14mL?

46. Units of Measurement: 7 Fundamental SI Units
Property
SI Unit and Standard of Measurement
Symbol
Length
meter m
Mass
kilogram kg
Time
second s
Temperature
Kelvin K
Amount of Substance
mole
mol
Current
ampere A
Luminous Intensity
candela cd

47. Derived Units Property Meaning Derived Unit Symbol Area l x w
Area
l x w
square meter m2
m x m
Volume
l x w x h
cubic meter m3
m x m x m
Volume (liquid)
cubic decimeter
dm3
dm x dm x dm
Force
mass x acceleration
newton N
1N = 1kg-m/s2
Pressure
force/area
pascal Pa
1Pa = 1N/m2
Energy
force x distance
joule J
1J = 1N-m
Frequency
cycles/second
hertz Hz
1Hz = 1wave cycle/second
Density
mass/volume
m/s, km/hr, m/min, etc.
Speed
distance/time
kg/m3, g/cm3, g/mL, etc

48. SFs, Rounding, SN Examples: How many significant figures? 99,000
2 sig figs
99,000.
5 sig figs
0.0099
2 sig figs
0.0990
3 sig figs

49. Practice http://studymaths.co.uk Worksheets tab Select numbers
Lesson 47, 32,4