1. Scientific Measurement
Chapter 2 Sec 2.3
Scientific Measurement

2. Vocabulary 14. accuracy 15. precision 16. percent error
17. significant figures
18. scientific notation
19. directly proportional
20. inversely proportional

3. Chapter 2 Objectives Distinguish between accuracy and precision.
Section 3 Using Scientific Measurements
Chapter 2
Objectives
Distinguish between accuracy and precision.
Determine the number of significant figures in measurements.
Perform mathematical operations involving significant figures.
Convert measurements into scientific notation.
Distinguish between inversely and directly proportional relationships.

4. 2.3 Measurements and Their Uncertainty
A measurement is a quantity that has both a number and a unit
Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct.
International System of Measurement (SI) typically used in the sciences

5. Accuracy and Precision
Accuracy is the closeness of a measurement to the correct (accepted) value of quantity measured
Precision is a measure of how close a set of measurements are to one another
To evaluate the accuracy of a measurement, the measured value must be compared to the correct value.
To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements

6. Accuracy and Precision

7. Accuracy and Precision
Which target shows:
1. an accurate but imprecise set of measurements?
2. a set of measurements that is both precise and accurate?
3. a precise but inaccurate set of measurements?
4. a set of measurements that is neither precise nor accurate?

8. Where do these measurements come from?
Recording Measurements

9. Accuracy and Precision, continued
Section 3 Using Scientific Measurements
Chapter 2
Accuracy and Precision, continued
Error in Measurement
Some error or uncertainty always exists in any measurement.
skill of the measurer
conditions of measurement
measuring instruments

10. F. Making Good Measurements
We can do 2 things:
1. Repeat measurement many times
- reliable measurements get the same number over and over
- this is PRECISION

11. F. Making Good Measurements
2. Test our measurement against a “standard”, or accepted value
- measurement close to accepted value is ACCURACY

12. Accuracy and Precision, continued
Section 3 Using Scientific Measurements
Chapter 2
Accuracy and Precision, continued
Percentage Error
Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.

13. G. Determining Error 1. Error = experimental value – accepted value
*experiment value is measured in lab (what you got during experiment)
* accepted value is correct value based on references (what you should have gotten)
2. Percent error = [Value experimental – Valueaccepted] x 100%
Valueaccepted
* Can put formula on notecard

14. 2.3 Practice Problems- Accuracy and Precision
Chapter 2
Section 2 Units of Measurement
2.3 Practice Problems- Accuracy and Precision
Set C (p.43)
1. What is the percentage error for a mass measurement of 17.7 g, given that the correct value is 21.2 g?

15. 2.3 Practice Problems- Accuracy and Precision
Chapter 2
Section 2 Units of Measurement
2.3 Practice Problems- Accuracy and Precision
Set C (p.43)
2. A volume is measured experimentally as 4.26 mL. What is the percentage error, given that the correct value is 4.15 mL?

16. 2.3 Practice Problems- Accuracy and Precision
Chapter 2
Section 2 Units of Measurement
2.3 Practice Problems- Accuracy and Precision
Set C (handout)
3. Bruce’s three measurements are 19 cm, 20 cm, and 22 cm. Calculate the average value of his measurements and express the answer with the correct number of significant figures.
4. Pete’s three measurements are 20.9 cm, 21.0 cm, and 21.0 cm. Calculate the average value of his measurements and express the answer with the correct number of significant figures.
Multiply the answer to problem #3 by the answer to problem #4. Express the answer in scientific notation with the correct number of significant figures.
Whose measurements are more precise?
The actual length of the object is 20 cm. Whose measurements are more accurate?
What is the error of Pete’s average measurement?
What is the percentage error of Pete’s average measurement?
Four boards each measuring 1.5 m are laid end to end. Multiply to determine the combined length of the boards, expressed with the correct number of significant figures.

17. What is the measured value?
Significant Figures in Measurement all known digits + one estimated digit

18. Estimating Measurements
The hundredths place is somewhat uncertain. Leaving it our would be misleading. Must estimate cm or 6.36cm

19. Error Probably not EXACTLY 6.35 cm Within .01 cm of actual value.
6.35 cm ± .01 cm
6.34 cm to 6.36 cm
Even though the measurement is always uncertain it is important that you are very careful making your measurements and keep care of you equipment.

20. Significant Figures, continued
Section 3 Using Scientific Measurements
Chapter 2
Significant Figures, continued
Determining the Number of Significant Figures

21. H. Rules of Significant Figures
1. Every nonzero digit in a measurement is significant (1-9). Ex: 831 g = 3 sig figs
2. Zeros in the middle of a number are always significant. Ex: 507 m = 3 sig figs
3. Zeros at the beginning of a number are NOT significant. Ex: g = 2 sig figs

22. H. Rules of Significant Figures
4. Zeros at the end of a number are only significant if a decimal point is present.
Ex: g = 4 sig figs
240. = 3 sig figs
2400 g = 2 sig figs
g = 3 sig figs

23. Sig Fig Practice #1 How many significant figures in the following?
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
These all come from some measurements
3.29 x 103 s 
3 sig figs
cm 
2 sig figs
3,200,000 mL 
2 sig figs
This is a counted value
5 dogs 
unlimited

24. I. Significant Figures in Calculations
1. A calculated answer can only be as precise as the least precise measurement from which it was calculated
2. Exact numbers never affect the number of significant figures in the results of calculations (unlimited sig figs)
a) counted numbers Ex: 17 beakers
b) exact defined quantities Ex: 60 sec = 1min
Ex: avagadro’s number = 6.02 x 1023

25. I. Significant Figures in Calculations
3. multiplication and division: answer can have no more sig figs than least number of sig figs in the measurements used.
4. addition and subtraction:
a) decimal - answer can have no more decimal places than the least number of decimal places in the measurements used. (not sig figs)
b) whole number- answer rounded so final sig fig is in the same place as the leftmost uncertain digit.
ex: = 5800

26. Sec 2.3 Significant Figures

27. Rounding Sig Fig Practice #1
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 23 m2
100.0 g ÷ 23.7 cm3
4.22
g/cm3
0.02 cm x cm
0.05
cm2
710 m ÷ 3.0 s
240
m/s

28. Rounding Practice #2 Calculation Calculator says: Answer
3.24 m m
10.24
10.2 m
100.0 g g
76.26
76.3 g
0.02 cm cm
2.398
2.40 cm
710 m -3.4 m
706.6
707 m

29. Sec 2.3 Practice Problems – Significant Figures

30. Sec 2.3 Practice Problems – Significant Figures

31. Scientific Notation
An expression of numbers in the form m x 10n where m (coefficient) is equal to or greater than 1 and less than 10, and n is the power of 10 (exponent)

32. J. Rules of Scientific Notation
1. Multiplication – multiply the coefficients and add the exponents
Ex: (3x104) x (2x102) = (3x2) x = 6 x 106
2. Division – divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator
Ex: (3.0x105)/(6.0x102) = (3.0/6.0) x = 0.5 x 103 = 5.0 x 102

33. J. Rules of Scientific Notation
3. Addition – exponents must be the same and then add the coefficients
Ex: (5.4x103) + (8.0x102)
(8.0x102) = (0.80x103)
(5.4x103) + (0.80x103) = ( ) x 103 = 6.2 x 103
4. Subtraction – exponents must be the same and then subtract the coefficients

34. Sec 2.3 Practice Problems – Scientific Notation

36. Chapter 2 Direct Proportions
Section 3 Using Scientific Measurements
Chapter 2
Direct Proportions
Two quantities are directly proportional to each other if dividing one by the other gives a constant value.
read as “y is proportional to x.”

37. Section 3 Using Scientific Measurements
Chapter 2
Direct Proportion

38. Chapter 2 Inverse Proportions
Section 3 Using Scientific Measurements
Chapter 2
Inverse Proportions
Two quantities are inversely proportional to each other if their product is constant.
read as “y is proportional to 1 divided by x.”

39. Section 3 Using Scientific Measurements
Chapter 2
Inverse Proportion

40. Vocabulary 14. accuracy 15. precision 16. percent error
17. significant figures
18. scientific notation
19. directly proportional
20. inversely proportional