1. Using and Expressing Measurements
3.1
Using and Expressing Measurements
Using and Expressing Measurements
How do measurements relate to science?

2. Using and Expressing Measurements
3.1
Using and Expressing Measurements
A measurement is a quantity that has both a number and a unit.
it is important to be able to make measurements and to decide whether a measurement is correct.

3. Scientific Notation
UeoBC0 Scientific Notation Pre-Test

4. Scientific Notation
210, 000,000,000,000,000,000,000 This number is written in decimal notation. When numbers get this large, it is easier to write it in scientific notation Where is the decimal in this number?

5. 210, 000,000,000,000,000,000,000. Decimal needs moved to the left between the 2 and the 1 ( numbers that are between 1-10) When the original number is more than 1 the exponent will be positive. 2.1 x 1023 Exponents show how many places decimal was moved

6. Express 4.58 x 106 in decimal notation
Remember the exponent tells you how many places to move the decimal. The exponent is positive so the decimal is moved to the right
4,580, 000

7. express the number 0. 000000345 in scientific notation
express the number in scientific notation. Decimal moved between first 2 non-zero digits and will be moved 7 times 3.45 x The exponent is negative because the original number is a very small number

8. Express the following in scientific notation or standard notation
x x 106

9. Accuracy, Precision, and Error
3.1
Accuracy, Precision, and Error
Accuracy, Precision, and Error
What is the difference between accuracy and precision?

10. Accuracy, Precision, and Error
3.1
Accuracy, Precision, and Error
Accuracy and Precision
Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured.
Precision is a measure of how close a series of measurements are to one another.

11. Accuracy, Precision, and Error
3.1
Accuracy, Precision, and Error
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.

12. Accuracy, Precision, and Error
3.1
Accuracy, Precision, and Error
The distribution of darts illustrates the difference between accuracy and precision. a) Good accuracy and good precision: The darts are close to the bull’s-eye and to one another. b) Poor accuracy and good precision: The darts are far from the bull’s-eye but close to one another. c) Poor accuracy and poor precision: The darts are far from the bull’s-eye and from one another.

13. Accuracy, Precision, and Error
3.1
Accuracy, Precision, and Error
Determining Error
The accepted (Known) value is the correct value based on reliable references.
The experimental value is the value measured in the lab.
The difference between the experimental value and the accepted value is called the error.

14. Accuracy, Precision, and Error
3.1
Accuracy, Precision, and Error
The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%.
Experimental – known
Expressing very large numbers, such as the estimated number of stars in a galaxy, is easier if scientific notation is used.

15. Accuracy, Precision, and Error
3.1
Accuracy, Precision, and Error
Percent Error (Error) 3.00-measurement X

16. Accuracy, Precision, and Error
3.1
Accuracy, Precision, and Error
Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate.
The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate. There is a difference between the person’s correct weight and the measured value. Calculating What is the percent error of a measured value of 114 lb if the person’s actual weight is 107 lb?

17. REVIEW

18. REVIEW

19. % ERROR
The density of aluminum is known to be 2.7 g/ml. In the lab you calculated the density of aluminum to be 2.4 g/ml. What is your percent error?
What is 5.256X10-6 in standard format
What is in scientific notation

20. Significant Figures in Measurements
3.1
Significant Figures in Measurements
All measurement contains some degree of uncertainty.
The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.
Measurements must always be reported to the correct number of significant figures
Using pages – fill in your notes regarding the rules of significant figures

21. Counting Significant Figures
Number of Significant Figures
38.15 cm 4
5.6 ft 2
65.6 lb ___
m ___
Complete: All non-zero digits in a measured number are (significant or not significant).
Timberlake lecture plus

22. Timberlake lecture plus
Leading Zeros
Number of Significant Figures
0.008 mm 1
oz 3
lb ____
mL ____
Complete: Leading zeros in decimal numbers are (significant or not significant).
Timberlake lecture plus

23. Timberlake lecture plus
Sandwiched Zeros
Number of Significant Figures
50.8 mm 3
2001 min 4
0.702 lb ____
m ____
Complete: Zeros between nonzero numbers are (significant or not significant).
Timberlake lecture plus

24. Timberlake lecture plus
Trailing Zeros
Number of Significant Figures 25,000 in
200 yr 1
48,600 gal 3
25,005,000 g ____
Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders.
Timberlake lecture plus

25. Timberlake lecture plus
Learning Check
A. Which answers contain 3 significant figures?
) ) 4760
B. All the zeros are significant in
1) ) ) x 103
C. 534,675 rounded to 3 significant figures is
1) ) 535, ) 5.35 x 105
Timberlake lecture plus

26. Significant Figures in Calculations
A calculated answer cannot be more precise than the measuring tool.
A calculated answer must match the least precise measurement.
Significant figures are needed for final answers from
1) adding or subtracting
2) multiplying or dividing
Timberlake lecture plus

27. Timberlake lecture plus
Adding & Subtracting
The answer has the same number of decimal places as the measurement with the fewest decimal places.
one decimal place
two decimal places
26.54
answer one decimal place
Timberlake lecture plus

28. Timberlake lecture plus
Learning Check
In each calculation, round the answer to the correct number of significant figures.
A =
1) ) ) 257
B =
1) ) ) 40.7
Timberlake lecture plus

29. Timberlake lecture plus
Solution
A =
2) 256.8
B =
3) 40.7
Timberlake lecture plus

30. Multiplying and Dividing
Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.
Timberlake lecture plus

31. Multiplication + Division Answer should have the same number of significant figures as the measurement with the least. You may need to round your answer in order to achieve this

32. Timberlake lecture plus
Learning Check
A X 4.2 =
1) ) )
B ÷ =
1) ) ) 60
C X =
X 0.060
1) ) )
Timberlake lecture plus

33. Timberlake lecture plus
Solution
A X = 2) 9.2
B ÷ = 3) 60
C X = 2) X 0.060
Continuous calculator operation =
x  
Timberlake lecture plus

34. Significant Figures in Calculations
3.1
Significant Figures in Calculations
Rounding
To round a number, you must first decide how many significant figures your answer should have.
Your answer should be rounded to the number with the least amount of significant figures

35. How many significant figures are in the number
QUIZ
How many significant figures are in the number
b c. 690,000
2. Perform the following operations and report to the correct number of sig. figs
4.15 cm X 1.8 cm
5.6 x 107 x 3.60 x 10-3

36. 3.1

37. 3.1

38. 3.2

39. 3.2

40. 3.3

41. 3.3