1. Put lab sheet on corner of your desk for me to pick up “Significant Figures”
Do these in composition book:
– 101
3.25 X 25
/ 7.11

2. Accuracy vs. Precision and Significant Figures

3. Accuracy versus Precision
Accuracy refers to the proximity of a measurement to the true value of a quantity.
Precision refers to the proximity of several measurements to each other.

4. Significant Figures
The term significant figures refers to digits that were measured.
The more significant figures, the greater the certainty implied for the measurement.
When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.

5. Need your ws out to go over from yesterday
How do you feel about sig fig’s?

6. Rules: Significant Figures
All nonzero digits are significant
Zeroes between two significant figures are themselves significant or 40.6
Zeroes at the beginning of a number are never significant
Zeroes at the end of a number are significant if a decimal point is written in the number
Zeroes at the end of a number are not significant if a decimal point is absent

7. Rules: Significant Figures
The USA trick sums up all the rules for you…
Pacific Ocean
Atlantic Ocean
Decimal is Present
Decimal is Absent
Start counting significant figures in the direction the arrow points
The first non-zero number you come to is the first significant figure, and then everything after is also significant

8. Significant Figures: Examples
How many significant figures?
a) km
b) s
c) L
d) 40 pm
e) kg
f) x 102 ms

9. Significant Figures: Examples
How many significant figures?
a) km
b) s
c) L
d) 40 pm
e) kg
f) x 102 ms 4 5 5 1 4 4

10. Controlling Number of Significant Figures
If rounding is necessary, look at the leftmost digit to be dropped off. If it is…
5 or greater, round the digit to its left up
457.3 expressed as 2 SF becomes 460
NOTE: expressed as 2 SF is NOT 46! DO NOT move the decimal place when you are rounding!
4 or less, leave the digit to its left as it is
454.1 expressed as 2 SF becomes 450
If more significant figures are required, add zero(s) to the end
320 expressed as 4 SF becomes 320.0
Scientific notation can always be used to express the correct number of significant figures.
54039 expressed as 3 SF becomes 5.40 x 104

11. 2) Add X10 to the power you moved the decimal
Examples: Significant Figures
Steps: 1) identify significant figures & keep that many in the coefficient
2) Add X10 to the power you moved the decimal
Express each as scientific notation:
a) km
b) s
c) L
d) 40 pm
e) kg
f) x 102 ms

12. Examples: Significant Figures
Express each as three significant figures:
a) km
b) s
c) L
d) 40 pm
e) kg
f) x 102 ms
3.77 km or x 100 km
s or x 10-3 s
L or x 105 L
40.0 pm or x 101 pm
3.50 x 103 kg
513 ms or x 102 ms

13. Significant Figures in Calculations
When carrying measured quantities through calculations,
the least certain measurement limits the certainty of the calculated quantity, and thereby determines the number of significant figures in the final answer.

14. Significant Figures in Calculations
When multiplication or division is performed,
The result contains the same number of SIGNIFICANT FIGURES as the measurement with the FEWEST significant figures.
134.7 x ÷ 1.9 =
The answer is 3100 or 3.1 x 103 because 1.9 has only two significant figures.
four significant
figures
five significant
figures
two significant
figures
Round the answer to two significant
figures (3100 or 3.1 x 103)

15. Significant Figures in Calculations
When addition or subtraction is performed,
The result has the same number of DECIMAL PLACES as the measurement with the FEWEST decimal places.
50.62
5.343
The answer is because has only one decimal place.
two decimal places
three decimal places
one decimal place
Round off to one decimal place (437.1)

16. Significant Figures in Calculations
When rounding:
Do NOT round until the final step of a multiplication/division problem
Do NOT round until the final step of an addition/subtraction problem
Exact numbers have an infinite number of significant figures (so don’t use them to determine significant figures)

17. Examples: Significant Figures in Calculations
b) 64.1 * =
c) ( – ) ÷ =

18. Examples: Significant Figures in Calculations
68.42
68.4
a) =
b) 64.1 * =
c) ( – ) ÷ =
3,237,050
3,240,000 or
3.24 x 106
2.827 x 10-5