1. Chapter 1 Measurement and Problem Solving
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2. Units of Chapter 1 Why and How We Measure
SI Units of Length, Mass, and Time
More about the Metric System
Unit Analysis
Unit Conversions
Significant Figures
Problem Solving
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3. 1.1 Why and How We Measure
Physics attempts to describe nature in an objective way through measurement.
Measurements are expressed in units; officially accepted units are called standard units.
Major systems of units:
Metric
British (used by the U.S., but no longer by the British!)
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4. 1.2 SI Units of Length, Mass, and Time
Length, mass, and time are fundamental quantities; combinations of them will form all the units we will use through Chapter 14.
In this text, we will be using the SI system of units, which is based on the metric system.
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5. 1.2 SI Units of Length, Mass, and Time
SI unit of length: the meter. The original definition is on the left, the modern one is on the right.
Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level),
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6. 1.2 SI Units of Length, Mass, and Time
SI unit of mass: the kilogram
Originally, the kilogram was the mass of 0.10 m3 of water.
Now, the standard kilogram is a platinum-iridium cylinder kept at the French Bureau of Weights and Measures.
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7. 1.2 SI Units of Length, Mass, and Time
SI unit of time: the second
The second is defined as a certain number of oscillations of the cesium-133 atom.
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8. 1.2 SI Units of Length, Mass, and Time
In addition to length, mass, and time, base units in the SI system include electric current, temperature, amount of substance, and luminous intensity.
These seven units are believed to be all that are necessary to describe all phenomena in nature.
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9. 1.3 More about the Metric System
The British system of units is used in the U.S., with the basic units being the foot, the pound (force, not mass), and the second.
However, the SI system is virtually ubiquitous outside the U.S., and it makes sense to become familiar with it.
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10. Learning Check
Give a couple of major differences between the SI and the British system.
One major difference is the decimal versus duodecimal basis. Another difference is that SI basic units are meters, kilograms and seconds, whereas the British system uses feet, pounds and seconds.

11. 1.3 More about the Metric System
In the metric system, units of the same type of quantity (length or time, for example) differ from each other by factors of 10. Here are some common prefixes:
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12. 1.3 More about the Metric System
The basic unit of volume in the SI system is the cubic meter. However, this is rather large for everyday use, so the volume of a cube 0.1 m on a side is called a liter.
Recall the original definition of a kilogram; one kilogram of water has a volume of one liter.
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13. Which of the following has the greatest volume?
Learning Check
Which of the following has the greatest volume?
2000 mL
1qt
2000 µl
1 L
1 quart= mL

14. Learning Check
Explain why 1 ml is equivalent to 1 cm3.
1 L=1000 mL and 1 L=1000 cm^3

15. 1.4 Unit Analysis
A powerful way to check your calculations is to use unit analysis.
Not only must the numerical values on both sides of an equation be equal, the units must be equal as well.
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16. 1.4 Unit Analysis
Units may be manipulated algebraically just as other quantities are.
Example:
Therefore, this equation is dimensionally correct.
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17. 1.5 Unit Conversions
A conversion factor simply lets you express a quantity in terms of other units without changing its physical value or size.
The fraction in blue is the conversion factor; its numerical value is 1.
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18. 1.6 Significant Figures
Calculations may contain two types of numbers: exact numbers and measured numbers.
Exact numbers are part of a definition, such as the 2 in d = 2r.
Measured numbers are just that—for example, we might measure the radius of a circle to be 10.3 cm, but that measurement is not exact.
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19. 1.6 Significant Figures SIGNIFICANT FIGURES
Significant figures are the numbers in a measurement that represent the certainty of the measurement, plus one number representing an estimate.
COUNTING ZEROS AS SIGNIFICANT FIGURES
Leading zeros are never significant figures.
Buried zeros are always significant figures.
Trailing zeros are generally significant figures（with decimal) .

20. 1.6 Significant Figures Significant figures in calculations:
1. When multiplying and dividing quantities, leave as many significant figures in the answer as there are in the quantity with the least number of significant figures.
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21. 1.6 Significant Figures
2. When adding or subtracting quantities, leave the same number of decimal places (rounded) in the answer as there are in the quantity with the least number of decimal places.

22. Learning Check
What volume in liters is a cube 40  cm on a side?
Express your answer using two significant figures
64 L

23. 1.7 Problem Solving
The flowchart at left outlines a useful problem-solving strategy. It can be used for most types of physics problems.
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24. 1.7 Problem Solving
The table at left describes several types of examples that are used in the text.
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25. Learning Check
A corner construction lot has the shape of a right triangle. If the two sides perpendicular to each other are 35  long and 46.3  long, what is the length of the hypotenuse?
Express your answer using two significant figures.
58.04

26. Accuracy and Precision
The accuracy of a measurement signifies how close it comes to the true (or accepted) value- that is, how nearly correct it is.

27. Precision
refers to the agreement among repeated measurements-that is, the “spread” of the measurements or how close they are together. The more precise a group of measurements, the closer together they are.

28. Review of Chapter 1
SI units of length, mass, and time: meter, kilogram, second
Liter: 1000 cm3; one liter of water has a mass of 1 kg
Unit analysis may be used to verify answers to problems
Significant figures – digits known with certainty, plus one
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29. Review of Chapter 1 Problem-solving procedure:
1. Read the problem carefully and analyze it.
2. Where appropriate, draw a diagram.
3. Write down the given data and what is to be found. (Make unit conversions if necessary.)
4. Determine which principle(s) are applicable.
5. Perform calculations with given data.
6. Consider if the results are reasonable.
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