1. Uncertainty in Measurement

2. Accuracy & Precision
Accuracy- describes how well the results of a measurement agree with an accepted value
Precision- the degree of exactness of a measurement, depends on the instrument used for measurement

3. Accuracy & Precision

4. Calculated to evaluate the ACCURACY of your experimental data:
% Error
Calculated to evaluate the ACCURACY of your experimental data:
% Error = Accepted – Experimental x Accepted

5. Example:
A book’s actual weight (accepted value) is 74.5 grams. You weigh the book and get 72.0 grams (experimental value).
74.5 g – 72.0 g x 100 = 3.35 % error
74.5 g
The lower your percent error, the more accurate your results!

6. Scientific Notation
A short way to express extremely large or small numbers
Expressed as the product of a number between 1 and 10 and a whole number power of 10.

7. For large numbers:
Move decimal to the left so that only ONE number is on the left of the decimal.
However many spaces you moved the decimal is the exponent of 10
Example: 28,000,000 = 2.8 x 107

8. For small numbers beginning in zero:
Move decimal to the right so that only ONE number is on the left of the decimal.
However many spaces you moved the decimal is the NEGATIVE exponent of 10.
Example: = x 10 -7

9. Significant Digits in Measurements
There are five rules or guidelines that should be applied in determining whether a digit in a measurement is significant.

10. Rule #1 Every nonzero digit in a measurement is always significant.
Example: m
3 significant digits g
5 significant digits

11. Rule #2 Zeros appearing between nonzero digits are significant.
Example: m
4 significant digits
1.503 g g
5 significant digits

12. Rule #3
Leading zeros are never significant. They serve as placeholders only.
Example: m
2 significant digits
0.421 m
3 significant digits m

13. Rule #4
Trailing zeros are only significant if the decimal point is written.
Example: 70 m
1 significant digit
70.0 m
3 significant digits
27, 000 cm
2 significant digits

14. Rule #5
Counting numbers and exactly defined quantities have an unlimited number of significant digits.
Example: 20 books
∞ number
1 hour = 60 minutes

15. Review
How many significant digits are in each of the following measurements?
a. 123 m b m c m
d m e. 22 metersticks f. 30 m
g m h m

16. Significant Figures in Calculations
Calculated values must be rounded so that they are consistent with the measurements from which they were calculated.

17. Multiplication and Division
In calculations involving multiplication and division, answers should be rounded so that they contain the same number of significant digits as the measurement with the least number of significant digits.
Example: m x 0.34 m =
m / 8.4 m =

18. Addition and Subtraction
The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.
Example: m m m =
m – m =

19. Review
Measure and calculate the length of the perimeter of your note card. Round your answer to the correct number of significant digits.
Measure and calculate the area of your note card (length x width). Round your answer to the correct number of significant digits.
Calculate the number of minutes spent in school in a 5 day week.

20. Quiz: Significant Digits

21. Write the following number in correct scientific notation.
How many significant digits are in each of the measurements below:
1) 100 m 2) m/s 3) m
4) 2.0 x 1011 m/s 5) 50 metersticks 6) s
Solve the following problems and round to the correct number of significant digits.
7) cm cm
8) cm x 0.18 cm
9) m2 ÷ m
10) cm – cm
Write the following number in correct scientific notation.
11) µm