1. Do Now & Announcements Take out HW to be checked
Work on Do Now. Take out a calculator when done
Unit 1 Test MON 8/31
Today: Significant Figures & Density
Tomorrow: Measurement Lab

2. The Concept of Error 100 m dash 1912 record: 10.6 seconds
Usain Bolt 100 m dash: 9.58 seconds

3. The Concept of Error Michael Phelps 100 m butterfly:
50.58 seconds—beats 2nd place Milorad Cavic by seconds!

4. The Concept of Error 3 4
Different people may report a different measurement when estimating the last digit

5. The Concept of Error
With each measurement, there is a degree of uncertainty/estimation beyond the markings
The last digit in a measurement is called the uncertain digit
Significant figures include all measured digits + the uncertain digit
The more significant figures, the more precise the measurement

6. Significant Figures All non-zero numbers are ALWAYS significant
15=2 sig figs
145=3 sig figs

7. Significant Figures
Zeros between nonzero digits (squished zeros) are ALWAYS significant
105=3 sig figs
5005=4 sig figs
ALL zeros to the left of the first nonzero are NOT significant
0.0005=1 sig fig
0.0505=3 sig figs

8. Sig Fig Clarifications
If there is a decimal point, the 0’s at the end of the number DO count
= 5 sig figs
If there is no decimal point, the 0’s at the end of the number DO NOT count!
91010 = 4 sig figs
For scientific notation, only count the sig figs for the decimal part (not the x 10x part)

9. Pacific-Atlantic Method for Counting Significant Figures
If the decimal point is present, start counting digits from the Pacific (left) side, starting with the first non-zero digit
If the decimal point is absent, start counting digits from the Atlantic (right) side, starting with the first nonzero digit

10. How Many Sig Figs? 4 2 2 4 5 8 3 2 2 4 1234 ________ 0.023 ________
________
0.023 ________
890 ________
91010 ________
________
________
________
3.4 x 104 ________
9.0 x 103 ________
9.010 x 10-2 ________ 2 2 4 5 8 3 2 2 4

11. Calculating with Significant Figures
Adding and Subtracting:
Count the number of decimal places for each measurement.
Round the final answer to the lowest number of decimal places.

12. Original Problem. Label Sig Figs!
Raw Answer
Final Answer w/ Proper # of Sig figs
640. –
327.8, 617, 546

13. Calculating with Significant Figures
Multiplying and Dividing:
Count the number of significant figures for each measurement
Round the final answer to the lowest number of significant figures

14. Original Problem. Label Sig Figs!
Raw Answer
Final Answer w/ Proper # of Sig figs
1.2 x 0.13
÷ 0.124
x 3.44
0.16, 3910, 2.79

15. Calculations with Units and Sig Figs
You can only add or subtract with like units. Your final answer will be expressed in that same unit
When multiplying/dividing:
Units can be different 
Express all units that did not cancel

16. Original Problem
Raw Answer
Final Answer w/ Proper Sig Figs and Units
3.482 cm cm cm
g g g
80.4 cm cm
106.5mL mL
48.2 cm × 1.6 cm × 2.12 cm
8.3 m × 4.0 m × m
64.34 cm3 ÷ cm
4.93 mm2 ÷ mm cm
28.32 cm
cm3
160 cm3
28.32 cm, cm, 63.9 cm, 77 mL, 160 cm3, 33 m3, cm2, mm

17. Volume Volume=amount of space an object takes up
Ways we can measure volume:
For liquids: using glassware
When using a graduated cylinder, read the value from the bottom of the meniscus

18. Volume Ways to measure volume
For regular solids: length x width x height

19. Volume Ways to measure volume For irregular solids: water displacement
40 mL
40-20 = 20 mL

20. Density
Density=the amount of mass in a given volume.

21. Which cube has a greater density?
Both cubes take up the same amount of space (volume), but cube A has more matter (mass)

22. Using the Density Formula
mass
density
volume

23. Density Practice: Round answer to proper number of sig figs!
If a sample of copper has a mass of 4.23 g and has a measured volume of 1.31 mL, what is its density?
A piece of metal with a mass of 147 g is placed in a 50 mL graduated cylinder. The water level rises from 20 mL to 41 mL. What is the density of the metal?
What is the volume of a sample that has a mass of 20 g and a density of 4 g/mL?
The mass of the element is g. The volume of the water it was placed in was 20.0 mL. The volume of the water after the element was placed in it was 21.5 mL. What is the density?  
3.23 g/mL, 7.0 g/mL, 5 mL, 6.82 g/mL