1. Chemistry Math Skills

2. Scientific Notation In Chemistry, you will see VERY LARGE numbers:
120,000,000,000,000,000,000
and
VERY SMALL numbers:

3. Scientific Notation 9.3 x 107 miles 1.24 x 10-5 km
Scientific Notation Examples:
6.5 X X 10-4
(Only list ONE number in front of decimal)
Scientific Notation
93,000,000 miles =
km =
9.3 x 107 miles
1.24 x 10-5 km
(negative exponent
if the number is less than one!)

4. Express Each in Scientific Notation:
0.135
12,500
3,500,000.
0.0306
1430
1.35 X 10-1
1.25 X 104
X106
3.06 X 10-2
7.2 X 10-6
1.430 X 103

5. Measurements and Sig Figs
Valid Measurements
0 cm 10
Ruler 1
3 cm
2 cm
Ruler 2
3.2 cm
3.1 cm
3.3 cm
Ruler 3
3.21 cm
3.19 cm
3.20 cm
Model 4

6. How to determine which numbers are “Significant Digits”
(SIG FIGS)

7. Rules for Counting Sig Figs - Details
Nonzero integers always count as significant figures.
3,456 m has
4 sig figs.
© Chemistry Collaborative edited from Sciencegeek.net

8. Rules for Counting Significant Figures - Details
Zeros
- Leading zeros do not count as
significant figures.
mL has
3 sig figs.
© Chemistry Collaborative edited from Sciencegeek.net

9. Rules for Counting Sig Figs - Details
Zeros
- Captive zeros always count as
significant figures.
16.07 atm has
4 sig figs.
© Chemistry Collaborative edited from Sciencegeek.net

10. Rules for Counting Sig Figs - Details
Zeros Trailing zeros are significant only if the number contains a decimal point.
9.300 km
4 sig figs.
9,300 m
2 sig figs.
0.320 L
3 sig figs.
20 kPa
1 sig fig.
© Chemistry Collaborative edited from Sciencegeek.net

11. Measurements and Sig Figs
Valid Measurements
0 cm 10
Ruler 1
3 cm
2 cm
Ruler 2
3.2 cm
3.1 cm
3.3 cm
Ruler 3
3.21 cm
3.19 cm
3.20 cm
Model 4

12. Sig Fig Practice #1 17.10 kg  4 sig figs 100,890 L  5 sig figs
How many significant figures in each of the following?
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
3.29 x 103 s 
3 sig figs
cm 
2 sig figs
3,200,000 mi 
2 sig figs
© Chemistry Collaborative edited from Sciencegeek.net

13. Get more Sig Fig review ONLINE 
Khan Academy is great online tutor!
Video – Sig Figs

14. Calculations and Sig Figs
There are guidelines for ROUNDING OFF your answer with the correct number of SigFigs

15. Calculations and Sig Figs
Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation.
6.38 x 2.0 =
12.76 (calculator)  13 (answer)
(2 sig figs)
Video review

16. Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m
100.0 g ÷ 23.7 cm3
g/cm3
4.22 g/cm3
0.02 cm x cm
cm2
0.05 cm2
710 m ÷ 3.0 s
m/s
240 m/s
lb x 3.23 ft
lb·ft
5870 lb·ft
1.030 g ÷ 2.87 mL
g/mL
0.359 g/mL
© Chemistry Collaborative edited from Sciencegeek.net

17. Calculations and Sig Figs
Addition and Subtraction: Your answer must be rounded off based on the number of decimal places in the least precise measurement.
6.8 cm cm
cm (calculator)
18.7 (answer)
Video review
© Chemistry Collaborative edited from Sciencegeek.net

18. Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m
100.0 g g
76.27 g
76.3 g
0.02 cm cm
2.391 cm
2.39 cm
713.1 L L L
709.2 L
lb lb lb lb
2.030 mL mL
0.16 mL
0.160 mL
© Chemistry Collaborative edited from Sciencegeek.net

19. Helpful Tip for Sig Figs
Know your rules!
Exact numbers have an infinite number of significant figures. (Important when doing conversions)
1 inch = cm, exactly
© Chemistry Collaborative edited from Sciencegeek.net

20. Is this you?

21. Have no fear!
ALL formulas you will use this year will ALWAYS be given to you on a reference sheet.

22. Using Formulas You will only have to ISOLATE a variable.
example: D = m/V
m = ?
V = ?
Khan Academy is great online tutor!
Video – Rearranging formula to Isolate aVariable

23. Density
Problem 1
A sample of aluminum is placed in a 25-mL graduated cylinder containing 10.5 mL of water. The level of the water rises to 13.5 mL. Density of Al is 2.7 g/cm3
What is the mass of the aluminum sample?

24. Density
Problem 2
A metal cube has a mass of 20.0 g and a volume of 5.2 cm3.
Is the cube made of pure aluminum?
Explain your answer.

25. Time for Density Lab!

26. With a partner, choose a small solid object (shell, pebble, bolt, etc)
First, pair share: how do we determine the volume of a solid object?
Keeping in mind that density = mass divided by volume (D = M/V), write out the steps needed for determining your object’s mass, volume, and density.
Write the calculations to determine your object’s density on a separate sheet of paper.
Trade your “steps” list and object with another pair and see if you get the same density.
Determine the percent error of your results:
Step 1: Calculate the error (subtract one value from the other) ignore any negative sign.
Step 2: Divide the error by the exact value (we get a decimal number)
Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)