1. Chapter 3- lec 1: Find the length of a paperclip with each of the three “rulers”
Ruler a
Ruler b
Ruler c
Were all of your measurements identical
2. Which measurement are you most uncertain of (required the greatest amount of estimation)?

2. Uncertainty in measurement
Measurements are only as precise as the instrument used.
Uncertainties of measurements are predictable and can be calculated.
They can be estimated to be half of the smallest division on a scale.
The last # which you estimate is the uncertain number.

3. Write down the following measurements. Include uncertainties.

4. Precision and Accuracy
Accurate- Measurements that are close to the “correct” value
Precise- Measurements that are close to each other.

5. Measurements… actual= 2.4cm
Student A
Student B
Trial 1
2.5 cm
1.8cm
Trial 2
2.4 cm
1.7cm
Trial 3
2.3 cm
Average:
2.4cm
1.76cm
Were either of the students accurate? Which one? WHY?
2. Were either of the students precise? Which one? WHY?

6. Percent error ·A way to explain the degree of error of a measurement.
·Uses the equation:
Accepted value = actual, theoretical, true, known
Example: Calculate the percent error of student B’s average

7. Units Notes Units: the scale that goes with numbers
There are 3 systems:
English – in America (ex. Foot, pound)
Metric- EVERYWHERE (ex. Meter, gram)
SI – for science
Based on metric

8. The Fundamental SI base units
measurement
unit
abbreviation
instrument
picture

9. The Fundamental SI base units
measurement
Length
unit
meter
abbreviation m
instrument
ruler
Picture

10. The Fundamental SI base units
measurement
Length
mass
unit
meter
kilogram
abbreviation m kg
instrument
ruler
Balance
picture

11. The Fundamental SI base units
measurement
Length
mass
volume
unit
meter
kilogram
liter
abbreviation m kg l
instrument
ruler
Balance
Graduated cylinder
picture

12. The Fundamental SI base units
measurement
Length
mass
volume
temperature
unit
meter
kilogram
liter
Kelvin
abbreviation m kg l K
instrument
ruler
Balance
Graduated cylinder
thermometer
picture

13. The Fundamental SI base units
measurement
Length
mass
volume
temperature
time
unit
meter
kilogram
liter
Kelvin
second
abbreviation m kg l K s
instrument
ruler
Balance
Graduated cylinder
thermometer
stopwatch
picture

14. Mass Mass = quantity of matter in an object.
Weight= force exerted on an object by gravity.
Which of these quantities does not change?

15. Exponents- Review
100 = 101 = 102 = 103 = 10-1 = 10-2 = 10-3 =

16. Exponents- Review
100 = = = = = = = .001

17. Scientific Notation (same as exponential notation)
It looks like: N X 10M
N is a number between 1 and 10
If M is positive it’s a # > 1
When M is negative it’s a # <1.

18. Ex. 1: The distance from the earth to the sun is 93,000,000 miles
- Sci not = 9.3 X 107
Notice 9.3 is between 1 and 10. And the exponent 7 is positive, because it represents a value larger than 1.

19. Ex. 2 The diameter of an atom is 0.00000000562cm
Scientific notation = 5.62x10-9
5.62 is between 1 and 10
The exponent is negative -9 because it represents a value smaller than 1.

20. Ex. 3: Convert 2.3 x 102 to standard notation.
The decimal moves over 2 places to make the number larger (its positive) =
230

21. Ex. 4: Ex:4 convert 3.6 x 10-4 in to standard notation

22. Ex. 5: Convert 2.54 x 106 into standard notation

23. Try these 4 on your own… Convert 0.0000003 to scientific notation
3. convert 3.4 x 107 to standard notation
4. Convert 2 x 10-3 to standard notation

24. Multiplication Multiply the coefficients and add the exponents.
(3 x 104) x (2 x 102) = (3 x 2) x = 6 x 106
(2.1 x 103) x (4.0 x 10–7) = (2.1 x 4.0) x 103+(–7) = 8.4 x 10–4

25. Division
Divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator.
3.0 x =
x 105–2 =
0.5 x 103 = 5.0 x 102
6.0 x 102
6.0

26. Addition and Subtraction
If you are not using a calculator, then the exponents must be the same (the decimal points must be aligned).
(5.4 x 103) + (8.0 x 102) = (5.4 x 103) + (0.80 x 103)
= ( ) x 103
= 6.2 x 103

27. Practice problems
Solve each problem and express the answer in scientific notation.
a. (8.0 x 10–2) x (7.0 x 10–5)
b. (7.1 x 10–2) + (5 x 10–3)

28. Practice problems
Solve each problem and express the answer in scientific notation.
a. (8.0 x 10–2) x (7.0 x 10–5) = 5.6 x 10–6
b. (7.1 x 10–2) + (5 x 10–3) = 7.6 x 10–2