1. Chapter 3 The Metric System by Christopher Hamaker
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2. The Metric System
The English system was used primarily in the British Empire and wasn’t very standardized.
The French organized a committee to devise a universal measuring system.
After about 10 years, the committee designed and agreed on the metric system.
The metric system offers simplicity with a single base unit for each measurement.
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3. Metric System Basic Units
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4. Original Metric Unit Definitions
A meter was defined as 1/10,000,000 of the distance from the North Pole to the equator.
A kilogram (1000 grams) was equal to the mass of a cube of water measuring 0.1 m on each side.
A liter was set equal to the volume of one kilogram of water at 4 C.
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5. Metric System Advantage
Another advantage of the metric system is that it is a decimal system.
It uses prefixes to enlarge or reduce the basic units.
For example:
A kilometer is 1000 meters.
A millimeter is 1/1000 of a meter.
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6. Metric System Prefixes
The following table lists the common prefixes used in the metric system:
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7. Metric Prefixes, Continued
For example, the prefix kilo- increases a base unit by 1000:
1 kilogram is 1000 grams.
The prefix milli- decreases a base unit by a factor of 1000:
There are 1000 millimeters in 1 meter.
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8. Metric Symbols
The names of metric units are abbreviated using symbols. Use the prefix symbol followed by the symbol for the base unit, so:
Nanometer is abbreviated nm.
Microgram is abbreviated mg.
Deciliter is abbreviated dL.
Gigasecond is abbreviated Gs.
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9. Nanotechnology
Nanotechnology refers to devices and processes on the 1–100 nm scale.
For reference, a human hair is about 100,000 nm thick!
A DNA helix is a nanoscale substance, with a diameter of about 1 nm.
Nanoscale hollow tubes, called carbon nanotubes, have slippery inner surfaces that allow for the easy flow of fluids.
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10. Metric Equivalents
We can write unit equations for the conversion between different metric units.
The prefix kilo- means 1000 basic units, so 1 kilometer is 1000 meters.
The unit equation is 1 km = 1000 m.
Similarly, a millimeter is 1/1000 of a meter, so the unit equation is 1000 mm = 1 m.
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11. Metric Unit Factors
Since 1000 m = 1 km, we can write the following unit factors for converting between meters and kilometers:
1 km or m
1000 m km
Since 1000 mm = 1 m, we can write the following unit factors:
1000 mm or m .
1 m mm
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12. Metric–Metric Conversions
We will use the unit analysis method we learned in Chapter 2 to do metric–metric conversion problems.
Remember, there are three steps:
Write down the unit asked for in the answer.
Write down the given value related to the answer.
Apply unit factor(s) to convert the given unit to the units desired in the answer.
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13. Metric–Metric Conversion Problem
What is the mass in grams of a 325 mg aspirin tablet?
Step 1: We want grams.
Step 2: We write down the given: 325 mg.
Step 3: We apply a unit factor (1000 mg = 1 g) and round to three significant figures.
325 mg x
= g
1000 mg
1 g
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14. Two Metric–Metric Conversions
A hospital has 125 deciliters of blood plasma. What is the volume in milliliters?
Step 1: We want the answer in mL.
Step 2: We have 125 dL.
Step 3: We need to first convert dL to L and then convert L to mL:
1 L and mL
10 dL L
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15. Two Metric–Metric Conversions, Continued
Apply both unit factors, and round the answer to three significant digits.
Notice that both dL and L units cancel, leaving us with units of mL.
125 dL x
= 12,500 mL x
10 dL
1 L
1000 mL
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16. Another Example
The mass of the Earth’s moon is 7.35 × 1022 kg. What is the mass expressed in megagrams, Mg?
We want Mg; we have 7.35 x 1022 kg.
Convert kilograms to grams, and then grams to megagrams.
7.35 x 1022 kg ×
= 5.98 x 1019 Mg x
1 kg
1000 g
1 Mg g
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17. Metric and English Units
The English system is still very common in the United States.
We often have to convert between English and metric units.
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18. Metric–English Conversion
The length of an American football field, including the end zones, is 120 yards. What is the length in meters?
Convert 120 yd to meters (given that yd = m).
120 yd x
= 110 m
1 yd
0.914 m
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19. English–Metric Conversion
A half-gallon carton contains 64.0 fl oz of milk. How many milliliters of milk are in a carton?
We want mL; we have 64.0 fl oz.
Use 1 qt = 32 fl oz, and 1 qt = 946 mL.
64.0 fl oz x
= 1,890 mL x
32 fl oz
1 qt
946 mL
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20. Compound Units Some measurements have a ratio of units.
For example, the speed limit on many highways is 55 miles per hour. How would you convert this to meters per second?
Convert one unit at a time using unit factors.
First, miles → meters
Next, hours → seconds
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21. Compound Unit Problem
A motorcycle is traveling at 75 km/hour. What is the speed in meters per second?
We have km/h; we want m/s.
Use 1 km = 1000 m and 1 h = 3600 s.
= 21 m/s x
1 km
1000 m
1 hr
3600 s
75 km hr
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22. Volume by Calculation
The volume of an object is calculated by multiplying the length (l) by the width (w) by the thickness (t).
volume = l x w x t
All three measurements must be in the same units.
If an object measures 3 cm by 2 cm by 1 cm, the volume is 6 cm3 (cm3 is cubic centimeters).
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23. Cubic Volume and Liquid Volume
The liter (L) is the basic unit of volume in the metric system.
One liter is defined as the volume occupied by a cube that is 10 cm on each side.
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24. Cubic and Liquid Volume Units
1 liter is equal to 1000 cubic centimeters.
10 cm x 10 cm x 10 cm = cm3
1000 cm3 = 1 L = 1000 mL.
Therefore, 1 cm3 = 1 mL.
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25. Cubic–Liquid Volume Conversion
An automobile engine displaces a volume of 498 cm3 in each cylinder. What is the displacement of a cylinder in cubic inches, in3?
We want in3; we have 498 cm3.
Use 1 in = 2.54 cm three times.
= 30.4 in3 x
1 in
2.54 cm
498 cm3 x
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26. Volume by Displacement
If a solid has an irregular shape, its volume cannot be determined by measuring its dimensions.
You can determine its volume indirectly by measuring the amount of water it displaces.
This technique is called volume by displacement.
Volume by displacement can also be used to determine the volume of a gas.
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27. Solid Volume by Displacement
You want to measure the volume of an irregularly shaped piece of jade.
Partially fill a volumetric flask with water and measure the volume of the water.
Add the jade, and measure the difference in volume.
The volume of the jade is 10.5 mL.
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28. Gas Volume by Displacement
You want to measure the volume of gas given off in a chemical reaction.
The gas produced displaces the water in the flask into the beaker The volume of water displaced is equal to the volume of gas.
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29. The Density Concept
The density of an object is a measure of its concentration of mass.
Density is defined as the mass of an object divided by the volume of the object.
= density
volume
mass
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30. Density
Density is expressed in different units. It is usually grams per milliliter (g/mL) for liquids, grams per cubic centimeter (g/cm3) for solids, and grams per liter (g/L) for gases.
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31. Densities of Common Substances
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32. Estimating Density
We can estimate the density of a substance by comparing it to another object.
A solid object will float on top of a liquid with a higher density.
Object S1 has a density less than that of water, but larger than that of L1.
Object S2 has a density less than that of L2, but larger than that of water.
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33. Calculating Density
What is the density of a platinum nugget that has a mass of g and a volume of 10.0 cm3 ? Recall, density is mass/volume.
= g/cm3
10.0 cm3 g
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34. Density as a Unit Factor
We can use density as a unit factor for conversions between mass and volume.
An automobile battery contains 1275 mL of acid. If the density of battery acid is 1.84 g/mL, how many grams of acid are in an automobile battery?
– We have 1275 mL; we want grams:
1275 mL x
= g mL
1.84 g
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35. Critical Thinking: Gasoline
The density of gasoline is 730 g/L at 0 ºC (32 ºF) and 713 g/L at 25 ºC (77 ºF). What is the mass difference of 1.00 gallon of gasoline at these two temperatures (1 gal = 3.784L)?
The difference is about 60 grams (about 2 %).
= 2760 g x
At 0 ºC: gal x
730 g L
3.784 L
1 gal
= 2700 g x
At 25 ºC: 1.00 gal x
713 g L
3.784 L
1 gal
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36. Temperature
Temperature is a measure of the average kinetic energy of the individual particles in a sample.
There are three temperature scales:
Celsius
Fahrenheit
Kelvin
Kelvin is the absolute temperature scale.
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37. Temperature Scales
On the Fahrenheit scale, water freezes at 32 °F and boils at 212 °F.
On the Celsius scale, water freezes at 0 °C and boils at 100 °C. These are the reference points for the Celsius scale.
Water freezes at 273 K and boils at 373 K on the Kelvin scale.
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38. Temperature Conversions
This is the equation for converting °C to °F.
This is the equation for converting °F to °C.
To convert from °C to K, add 273.
°C = K
= °F
°C x
100°C
180°F
( )
( )
180°F
100°C
= °C
(°F - 32°F) x
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39. Fahrenheit–Celsius Conversions
Body temperature is 98.6 °F. What is body temperature in degrees Celsius? In Kelvin?
K = °C = °C = 310 K
( )
180°F
100°C
= 37.0°C
(98.6°F - 32°F) x
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40. Heat
Heat is the flow of energy from an object of higher temperature to an object of lower temperature.
Heat measures the total energy of a system.
Temperature measures the average energy of particles in a system.
Heat is often expressed in terms of joules (J) or calories (cal).
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41. Heat Versus Temperature
Although both beakers below have the same temperature (100 ºC), the beaker on the right has twice the amount of heat because it has twice the amount of water.
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42. Specific Heat
The specific heat of a substance is the amount of heat required to bring about a change in temperature.
It is expressed with units of calories per gram per degree Celsius.
The larger the specific heat, the more heat is required to raise the temperature of the substance.
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43. Chapter Summary
The basic units in the metric system are grams for mass, liters for volume, and meters for distance.
The base units are modified using prefixes to reduce or enlarge the base units by factors of ten.
We can use unit factors to convert between metric units.
We can convert between metric and English units using unit factors.
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44. Chapter Summary, Continued
Volume is defined as length x width x thickness.
Volume can also be determined by displacement of water.
Density is mass divided by volume.
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45. Chapter Summary, Continued
Temperature is a measure of the average energy of the particles in a sample.
Heat is a measure of the total energy of a substance.
Specific heat is a measure of how much heat is required to raise the temperature of a substance.
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