1. Another thing you’ll use basically every day from now on.
Significant Figures
Another thing you’ll use basically every day from now on.

2. What is “one gram”? What is the mass? Exactly one gram?
Do they have the same mass? Exactly?
[Picture of paperclip on centigram balance.], [picture of calibration weight on centigram balance.]

3. Now do they both still have mass of one gram?
Pictures of both weight and paperclip on analytical balance

4. Measurements vs Exact numbers
Measurements are never exact. They are always rounded.
example
Exact numbers are not rounded off.
1 dozen = 12
20 people
1km = 1, 000 m
Significant figures are used to determine how specific a measurement is.
ex. 56,000 people attend a soccer game.
What place is this value rounded to? Which is the estimated digit?

5. Some instruments do the rounding for you.
What place are each of these rounded to?
What are the estimated digits?

6. Counting significant figures.
Find first non-zero digit
Is there a decimal point?
No  Find the last non-zero digit. (It’s estimated.)
1020  3 sig figs
Yes  Find the last digit. (It’s estimated.)
 5 sig figs
How many sig figs are there in each measurement?
56,000
1.00 g g
120 m
120.0 m
120. m

7. Sig Figs in Calculations
ex. This room is 9.1 m wide and m long. Find area.
9.1 m × m = m2
What is this rounded to? Make sense?
Multiplication and Division: The answer should have the same number of sig figs as least specific number in problem
Round to 2 sig figs, so
m2 = 110 m2

8. Sig Figs in Calculations, cont.
ex. The sun is 146,000,000,000 m away. If you go upstairs, you get 3 m closer. Find new distance.
146,000,000,000m – 3m = 100,000,000,000m
Make sense? Nope.
Addition and Subtraction: Answer is rounded to same place as least specific number in problem
146,000,000,000 – 3 = 145,999,999,997
Round to billions place, so 146,000,000,000
ex =
More practice