1. How to determine and use the proper sig. figs.
Significant Figures
How to determine and use the proper sig. figs.

2. What is a significant figure?
There are 2 kinds of numbers:
Exact numbers
Measured numbers

3. What is a significant figure?
1) Exact: don’t come in fractions or decimals!!!
Ex: humans
Ex: bacterial colonies on a petri dish

4. What is a significant figure?
On the other hand…not everything is so easy…sometimes you have to …
Approximate: A close guess that is in the ball park.

5. When to use Significant figures
2) Measured numbers
Using a tool/ device to measure…you must ask yourself what are the limits of the tool/ device.
Ex:

6. When to use Significant figures
You could measure Arrow “A” as 3.9cm.
But to some mathematicians 3.9cm, or 3.90cm is the same. A

7. But, to a scientist 3.9cm and 3.90cm is NOT the same
Key difference
But, to a scientist 3.9cm and 3.90cm is NOT the same

8. Uncertainty is defined as ½ of the smallest certain unit
The limit of the device!
Uncertainty is defined as ½ of the smallest certain unit
If a Centimeter Ruler was used…
Arrow
Length ± 0.5cm*
Arrow “A”
3.9
Arrow “B”
3.4 A B
*You should report the uncertain digit
If a Millimeter Ruler was used…
Arrow
Length ± 0.5mm*
Arrow “A”
39.1
Arrow “B”
33.8

9. Uncertainty is defined as ½ of the smallest certain unit
The limit of the device!
Uncertainty is defined as ½ of the smallest certain unit
What about electronic devices?*
Digital Balances:
The last digit is uncertain.
For example: The mass of the powder is 5.00g ± 0.05
*some electronic devices have published uncertainty,
If you have access to the manual, refer to it.

10. How do I know how many Sig Figs?
Basic Decimal Rules
If no Decimal, then start counting at the first NON zero, and stop counting at the last NON zero!
30  1 sig fig
303  3 sig figs
3030  3 sig figs

11. How do I know how many Sig Figs?
Basic Decimal Rules
If Decimal, then start counting at the first NON zero, and count until the end!
3.1  2 sig fig
3.03  3 sig figs
 4 sig figs
0.303  3 sig figs

12. How many sig figs? 7 40
0.5
7 x 105
7,000,000 1

13. How many sig figs here?
1.2
2100
56.76
4.00
0.0792
7,083,000,000 2 4 3

14. Identify the uncertain digit in each number?
1.2
2100
56.76
4.00
0.0792
7,083,000,000
1.2
2100
56.76
4.00
0.0792
7,083,000,000

15. How many sig figs here?
3401
2100
2100.0
5.00
8,000,050,000 4 2 5 3 6

16. How would you indicate uncertainty?
3401
2100
2100.0
5.00
8,000,050,000
3401 ±5
2100 ±500
±0.5
5.00 ±0.05 ±
8,000,050,000 ±50,000

17. What about calculations with sig figs?
Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

18. Add/Subtract examples
2.45cm + 1.2cm = 3.65cm,
Round off to = 3.7cm
which digit is uncertain?
3.7

19. Add/Subtract examples
7.432cm + 2cm = round to  9cm
which digit is uncertain?
9 cm

20. Multiplication and Division
Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

21. A couple of examples 56.78 cm x 2.45cm = 139.111 cm2 Round to  139cm2
which digit is uncertain?
139 cm2

22. A couple of examples 75.8cm x 9.6cm = ? Do the math and round to…
Which digit is uncertain?
How would you record uncertainty?

23. Sig fig Math!!!