1. Chapter 3 Scientific Measurement 3.1 Using and Expressing Measurements
3.2 Units of Measurement
3.3 Solving Conversion Problems
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2. Write the following in scientific notation 238,900 0.000365
Do Now:
Write the following in scientific notation
238,900
Solve each problem. Answer in scientific notation.
(4.5 x 104) + (6.3 x 103)
(4.5 x 104) - (6.3 x 103)
(4.5 x 104) x (6.3 x 103)
(4.5 x 104) ÷ (6.3 x 103)
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3. Coefficient x 10 exponent
Scientific Notation
Scientific notation: a number is written as the product of two numbers
Coefficient x 10 exponent
602,000,000,000,000,000,000,000 = 6.02 x 1023
Coefficient: 6.02
Exponent: 23
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4. Scientific Notation
The coefficient is always a number greater than or equal to one and less than ten.
60.2 x 1022
6.02 x 1023
602 x 1021
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5. Multiply the coefficients and add the exponents.
Scientific Notation
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
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6. Scientific Notation
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
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7. Addition and Subtraction
Scientific Notation
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
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8. Using Scientific Notation
Sample Problem 3.1
Using Scientific Notation
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)
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9. Using Scientific Notation
Sample Problem 3.1
Using Scientific Notation
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)
= 5.6 x 10–6
= 7.6 x 10–2
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10. Measure the length and width of an index card using a ruler.
Calculate the area of the index card.
Width
Length
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11. Measurement: quantity that has both a number and a unit.
Examples
Height: 66 inches
Age: 15 years
Body temperature: 37°C
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12. Significant Figures
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13. Significant Figures
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14. Any digit that gives us useful information is significant!!!
Significant Figures
Significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.
Any digit that gives us useful information is significant!!!
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15. Accuracy, Precision, and Error
Determining Error
Experimental value: value measured in the lab.
Accepted value: correct value for the measurement based on reliable references
Error = experimental value – accepted value vaue
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16. Accuracy, Precision, and Error
Determining Error
Percent error: the absolute value of the error divided by the accepted value, multiplied by 100.
Percent error =
error
accepted value
100 x
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17. Calculating Percent Error
Sample Problem 3.2
Calculating Percent Error
The boiling point of pure water is measured to be 99.1°C. Calculate the percent error.
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18. |experimental value – accepted value| _______________________________
Sample Problem 3.2
Percent error =
|experimental value – accepted value|
_______________________________
accepted value
X 100
|99.1°C – 100.0°C|
X 100 =
100.0°C
_______ =
100.0°C
X 100 = 0.9%
0.9°C
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19. Do Now:
What is the difference between the measurements 3 cm, 3.0 cm, and 3.00cm?
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20. Accuracy, Precision, and Error
Accuracy: a measure of how close a measurement comes to the actual or true value of whatever is measured.
Precision: a measure of how close a series of measurements are to one another, irrespective of the actual value.
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21. Atlantic – Pacific Rule
Significant Figures
Atlantic – Pacific Rule
Is there a decimal?
Pacific Atlantic
(Present) (Absent)
Start from LEFT Start from RIGHT
& count all #’s & count all #’s
from first nonzero from first nonzero
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22. Determining Significant Figures
Measurements - Use Atlantic – Pacific Rule
Count – Infinite number of sig figs
Defined quantities – Infinite number of sig figs
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23. Counting Significant Figures in Measurements
Sample Problem 3.3
Counting Significant Figures in Measurements
How many significant figures are in each measurement?
123 m
40,506 mm
x 104 m
22 metersticks m
98,000 m
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24. Counting Significant Figures in Measurements
Sample Problem 3.3
Counting Significant Figures in Measurements
How many significant figures are in each measurement?
123 m 3 sig figs
40,506 mm 5 sig figs
x 104 m 5 sig figs
22 metersticks infinite
m 4 sig figs
98,000 m 2 sig figs
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25. Significant Figures in Calculations
Calculated answers CANNOT be more precise than the least precise measurement from which it was calculated.
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26. Significant Figures in Calculations
Addition and Subtraction
Round to the same number of decimal places (not digits) as the measurement with the least number of decimal places.
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27. Significant Figures in Addition and Subtraction
Sample Problem 3.5
Significant Figures in Addition and Subtraction
Perform the following calculation. Give each answer to the correct number of significant figures.
a meters meters meters
b meters – meters
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28. Significant Figures in Addition and Subtraction
Sample Problem 3.5
Significant Figures in Addition and Subtraction
Perform the following addition and subtraction operations. Give each answer to the correct number of significant figures.
a meters meters meters
b meters – meters
= meters
= meters
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29. Significant Figures in Calculations
Multiplication and Division
Round answer to the same number of significant figures as the measurement with the LEAST number of significant figures.
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30. Significant Figures in Multiplication and Division
Sample Problem 3.6
Significant Figures in Multiplication and Division
Perform the following operations. Give the answers to the correct number of significant figures.
a meters x 0.34 meter
b meters x 0.70 meter
c meters2 ÷ 8.4 meters
d meter2 ÷ meter
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31. Significant Figures in Multiplication and Division
Sample Problem 3.6
Significant Figures in Multiplication and Division
Perform the following operations. Give the answers to the correct number of significant figures.
a meters x 0.34 meter = 2.6 meters2
b meters x 0.70 meter = 1.5 meters2
c meters2 ÷ 8.4 meters = 0.29 meter
d meter2 ÷ meter = 18.3 meters
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32. Sample Problem 3.4
Do Now:
Round each measurement to the number of significant figures shown in parentheses. Write the answers in scientific notation.
a meters (four)
b meter (two)
c meters (two)
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33. Sample Problem 3.4
Do Now:
Round each measurement to the number of significant figures shown in parentheses. Write the answers in scientific notation.
a x 102 meters
b. 1.8 x 10-3 meter
c. 8.8 x 103 meters
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34. END OF 3.1
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