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. 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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3. 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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4. The radius of a gold atom is 0.000000000135 meters.
Scientific Notation
The radius of a gold atom is meters.
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5. There are 100,000,000,000 stars in the Milky Way.
Scientific Notation
There are 100,000,000,000 stars in the Milky Way.
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6. 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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7. 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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8. 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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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. 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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13. 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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14. 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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15. Accuracy, Precision, and Error
Accuracy: how close a measurement comes to the actual or true value
Precision: how close measurements are to one another
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16. 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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17. 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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18. 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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19. 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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20. Significant Figures in Calculations
Calculated answers CANNOT be more precise than the least precise measurement from which it was calculated.
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21. 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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22. 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.
a meters meters meters
b meters – meters
= meters
= meters
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23. 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.
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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24. END OF 3.1
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