1. Measurements and Calculations
Chapter 2
Measurements and Calculations

2. Quantitative observation. Has 2 parts – number and unit.
Measurement
Quantitative observation.
Has 2 parts – number and unit.
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3. Technique used to express very large or very small numbers.
Expresses a number as a product of a number between 1 and 10 and the appropriate power of 10.
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4. Using Scientific Notation
The number of places the decimal point is moved determines the power of 10. The direction of the move determines whether the power of 10 is positive or negative.
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5. Using Scientific Notation
If the decimal point is moved to the left, the power of 10 is positive.
If the decimal point is moved to the right, the power of 10 is negative.
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6. Express the following numbers in scientific notation: 0.0000671; 72.
The World’s population is estimated to be 7,187,000,000 people. Express this number in scientific notation.
Express the following numbers in scientific notation: ; 72.
Express the following numbers in standard notation: x 10-7; 9.5 x 104.
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7. Nature of Measurement
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8. The Fundamental SI Units
Physical Quantity
Name of Unit
Abbreviation
Mass
kilogram kg
Length
meter m
Time
second s
Temperature
kelvin K
Electric current
ampere A
Amount of substance
mole
mol
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9. Prefixes Used in the SI System
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10. Length
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11. Measure of the amount of 3-D space occupied by a substance.
Volume
Measure of the amount of 3-D space occupied by a substance.
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12. Measure of the amount of matter present in an object.
Mass
Measure of the amount of matter present in an object.
Weight
Measure of the gravitational pull on an object.
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13. A gallon of milk is equal to about 4 L of milk.
Concept Check
Choose the statement(s) that contain improper use(s) of commonly used units (doesn’t make sense)?
A gallon of milk is equal to about 4 L of milk.
A 200-lb man has a mass of about 90 kg.
A basketball player has a height of 7 m tall.
A nickel is 6.5 cm thick.
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14. Measurement of Length Using a Ruler
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15. A digit that must be estimated is called uncertain.
A measurement always has some degree of uncertainty.
Record the certain digits and the first uncertain digit (the estimated number).
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16. Rules for Counting Significant Figures
Nonzero integers always count as significant figures.
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17. Rules for Counting Significant Figures
Leading zeros are zeros that precede all the nonzero digits. These do not count as significant figures.
Captive zeros are zeros between nonzero digits. These always count as significant figures.
Trailing zeros are zeros at the right end of the number. They are significant only if the number contains a decimal point.
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18. Exponential Notation
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19. Rules for Counting Significant Figures
Exact numbers have an infinite number of significant figures.
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20. Rules for Rounding Off
If the digit to be removed is less than 5, the preceding digit stays the same. If the digit to be removed is equal to or greater than 5, the preceding digit is increased by 1.
In a series of calculations, carry the extra digits through to the final result and then round off.
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21. Significant Figures in Mathematical Operations
1. For multiplication or division, the number of significant figures in the result is the same as that in the measurement with the smallest number of significant figures.
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22. Significant Figures in Mathematical Operations
2. For addition or subtraction, the limiting term is the one with the smallest number of decimal places.
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23. Concept Check
You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred).
How would you write the number describing the total volume?
What limits the precision of the total volume?
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24. An impossibly regular, paved walkway mysteriously appears overnight; leading out of Seattle. Careful measurement shows this walkway to be 15,432 meters long and 0.42 meters wide. To the correct number of significant figures, what area is covered by walkway? How would this number change if the walkway were 0.41 meters wide? meters wide?
By the next morning, this walkway has grown 0.42 meters. To the correct number of significant figures, how long is it now?
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25. Use when converting a given result from one system of units to another.
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26. A golfer putted a golf ball 6. 8 ft across a green
A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? How many centimeters?
What is the volume of a 1.25 gallon jug in cubic centimeters? Cubic inches? (1 L = qts)
An iron sample has a mass of 4.50 lb. What is the mass of this sample in grams? (1 kg = lbs)
If an oxygen molecule is moving at 4.78 x 104 cm/s, what is its speed in mi/hr?
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27. Three Systems for Measuring Temperature
Fahrenheit
Celsius
Kelvin
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28. The Three Major Temperature Scales
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29. Converting Between Scales
The normal body temperature for a dog is approximately 102oF. What is this equivalent to on the Kelvin temperature scale?
At what temperature does C = F?
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30. Mass of substance per unit volume of the substance.
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32. Measuring the Volume of a Solid Object by Water Displacement
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33. Example
A certain mineral has a mass of 17.8 g and a volume of 2.35 cm3. What is the density of this mineral?
What is the mass of a 49.6 mL sample of a liquid, which has a density of 0.85 g/mL?
Copper has a density of 8.96 g/cm3. If 75.0 g of copper is added to 50.0 mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise?
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36. Summary of Topics: Chapter 2
Significant figures
Scientific notation
Metric units
Measured numbers, exact numbers
Dimensional analysis (conversions)
Temperature
Density
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