1. Significant Figures

2. Measured Numbers
When you use a measuring tool is used to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers.

3. Exact Numbers Obtained when you count objects
2 soccer balls
1 watch
4 pizzas
Obtained from a defined relationship
1 foot = 12 inches
1 meters = 100 cm
Not obtained with measuring tools

4. Exact numbers are obtained by
Counting
Definition
Measuring
Counting & Definition

5. Measured numbers are obtained by
Measuring
Counting
Definition

6. Classify as exact or measured number : Gold melts at 1064 Celsius.

7. Classify as exact or measured: 1 yard = 3 feet

8. Classify as exact or measured: A red blood cell with diameter 6 x 10 -4cm.

9. Classify as exact or measured: There were six hats on the shelf.

10. Classify as exact or measured: A can of soda contains 355 mL of soda.

11. Uncertainty in Measurement
The numbers reported in a measurement are limited by the measuring tool
Significant figures in a measurement include the known digits plus one estimated, or uncertain digit

12. This nail is 6.3 centimeters long for sure, but what exactly
is the value of the hundredths place
– 6.35, 6.36, 6.37?

13. “Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.”
In the nail example, the hundredths place (3.36, the 6) is uncertain, or estimated.
A SIGNIFICANT FIGURE IS NOT ALWAYS CERTAIN – THE LAST DIGIT OF ANY MEASUREMENT IS ESTIMATED!!!

14. Rules For Significant Figures
All non-zero digits are significant
Examples:
significant figures
significant figures

15. How many significant figures in 896.76
B. 3
C. 4
D. 5

16. Rules For Significant Figures
2) Zeros between numbers (sandwiched zeros) are all significant
Example:
304 – 3 significant digits
– 5 significant digits

17. How many significant figures in 1,043?2 3 4

18. Rules For Significant Figures
3) Any zero appearing in front of a non-zero digit is NOT significant (regardless of a decimal)
Example:
0.876 – 3 significant digits
– 2 significant digits

19. How many significant figures in 0.00081 3 4 5

20. Rules for significant figures
4) Zeros at the end of a number AND to the right of a decimal point are significant
Examples:
72.00 – 4 significant figures
– 10 significant figures

21. How many significant figures in 5.60002 4 5
Help, I’m confused!

22. Rules For Significant Figures
5. A) Zeros at the end of the number WITHOUT a decimal place are NOT significant.
Example:
3,000 – 1 significant figure
560 – 2 significant figures

23. How many significant figures does 453,000 have?2 3 4 6

24. Rules For Significant Figures
5 B) Zeros at the end of a number to the LEFT of a decimal point are significant
Example:
- Has three significant figures
4,000. – Has four significant figures

25. How many significant figures does 1,000. have?2 3 4

26. How many sig figs does 305.00 have?2 3 5
Help! I’m confused!

27. How many sig figs does 0.009 have?1 2 3 4

28. How many sig figs does 5,600. 1 2 3 4

29. Sig Figs in Calculations
A calculated answer cannot be more precise than the measuring tool.
A calculated answer must match the least precise measurement.
Significant figures are needed for final answers from
1) adding or subtracting
2) multiplying or dividing

30. Sig Figs and Addition/Subtraction
The answer has the same number of decimal places as the measurement with the fewest decimal places.
one decimal place
two decimal places
26.54
answer one decimal place

31. Round the answer to the correct number of significant figures. 235
256.75
256.8
257

32. Round the answer to the correct number of significant figures 58
40.725
40.73
40.7

33. Multiplying and Dividing with Sig Figs
Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

34. 2.19 X 4.2 9
9.2
9.198

35. ÷ 0.07
61.58 62 60