1. Aim: Why are Significant Figures Important?
Do Now:
Read the ruler below. At what number is the pointer at. Be as accurate as possible.

2. Accuracy is how correct something is, or how close to the true value
Accuracy vs Precision
Accuracy
Precision
Accuracy is how correct something is, or how close to the true value
Precision is how close your measurements are to each other, or how consistent something is

3. Accuracy vs. Precision Match the following:
Low accuracy and High Precision
Low accuracy and low precision
High accuracy and high precision
High Accuracy and low precision
A. D. B. C.

4. Significant Figures All measurements are inaccurate due to:
Precision of measuring device
Human error
Faulty technique

5. Let’s try graduated cylinders
Look at the graduated cylinder below
What can you read with confidence?
56 ml
Now estimate the last digit
56.0 ml

6. One more graduated cylinder
Look at the cylinder below…
What is the measurement?
53.5 ml

7. Significant Figures Significant figures in a measurement include
all of the digits that are known precisely
plus one last digit that is estimated.

8. All non zero digits are ALWAYS significant
How to determine how many significant figures a measurement has Rule #1
All non zero digits are ALWAYS significant
How many significant digits are in the following numbers?
3 Significant Figures
5 SF
4 SF
274
25.632
8.987

9. Rule #2 All zeros between significant digits are ALWAYS significant
How many significant digits are in the following numbers?
3 SF
5 SF
4 SF
504
60002
9.077

10. Rule #3
Zeros after non-zero digits are significant when a decimal is present.
How many significant digits are in the following numbers?
32.0
19.000
3 SF
5 SF
7 SF

11. Rule #4 All zeros that act as place holders are NOT significant
Zeros before non-zero digits are not significant SF
Zero after non-zero digit with no decimal are not significant SF

13. For example 1 SF 1) 0.0002 3 SF 2) 6.02 x 1023 6 SF 3)100.000 2 SF
How many significant figures are in the following numbers?
1 SF
3 SF
6 SF
2 SF 1)
2) 6.02 x 1023 3)
4)150000
5) 800

14. Sig Fig Rounding Example:
Round the following measured number to
4 sig figs:

15. Sig Fig Rounding Example
Round the following measured number to
4 sig figs:

16. Sig Fig Rounding Example
Round the following measured number to
4 sig figs:
ANSWER:

17. Adding Significant Zeros
Sometimes a calculated answer requires more significant digits. Then one or more zeros are added.
Calculated Answer Zeros Added to
Give 3 Significant Figures

18. Practice Rounding Numbers

19. Significant Figures Round each to 3 sig figsb)
c) 2568
d) 2562
e) 8

20. Significant Figures Round each to 3 sig figs
a) ANSWER: 28.4
b) ANSWER:
c) ANSWER: 2570
d) ANSWER: 2560
e) ANSWER: 8.00

21. Addition and Subtraction
When adding or subtracting, use
The same number of decimal places in your final answer as the measurement with the fewest decimal places (least precise measurement).
Use rounding rules to adjust the number of digits in the answer.
one decimal place
two decimal places
26.54 calculated answer
answer with one decimal place

22. Multiplication and Division
When multiplying or dividing, use
The same number of significant figures in your final answer as the measurement with the fewest significant figures.
Rounding rules to obtain the correct number of significant figures.
Example:
x = = (rounded)
4 SF SF calculator SF

23. Calculations

24. Scientific Notation
Scientific Notation allows us to display massive and tiny numbers in a universal simple way.
Instead of writing 4,000,000
we would write 4.0 x 106
All we are doing is moving the decimal to the right of the first non-zero number
We then write x 10the number of places we moved the decimal
On a BIG number, we move the decimal left and the exponent is positive
On a LITTLE number, we move the decimal right and the exponent is negative

25. Converting to Scientific Notation
Example: Write 5,000,000,000 in scientific notation
Now we write 5.0 x 109 because we moved the decimal 9 places to the left

26. Converting to Scientific Notation
Example: Write in scientific notation
Now we write x 10-4 because we moved the decimal 4 places to the right

27. Scientific Notation Practice
Practice writing these in Scientific Notation:
Practice writing these in from Scientific Notation:
5) 8.2 x 102 6) 9.63 x ) 7.22 x 105 8) x 10-4
300
420
0.34

28. Scientific Notation and Calculators
Different ways calculators express scientific notation

29. Scientific Notations and Calculations
Whenever doing calculations on a calculator with scientific notation, ALWAYS put the scientific notation in parenthesis
Ex: (1.23 x 104 ) / (5.67 x 10-8)

30. Calculations