1.6: The International System of Units
- Page ID
- 165413
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- To recognize the SI base units and explain the system of prefixes used with them.
People who live in the United States measure weight in pounds, height in feet and inches, and a car’s speed in miles per hour. In contrast, chemistry and other branches of science use the International System of Units (also known as SI after Système Internationale d’Unités), which was established so that scientists around the world could communicate efficiently with each other. Many countries have also adopted SI units for everyday use as well. The United States is one of the few countries that has not.
Base SI Units
Base (or basic) units, are the fundamental units of SI. There are seven base units, which are listed in Table \(\PageIndex{1}\), Chemistry uses five of the base units: the mole for amount, the kilogram for mass, the meter for length, the second for time, and the kelvin for temperature. The degree Celsius (°C) is also commonly used for temperature. The numerical relationship between kelvins and degrees Celsius is as follows:
\[K = °C + 273 \label{Eq1}\]
Property | Unit | Abbreviation |
---|---|---|
length | meter | m |
mass | kilogram | kg |
time | second | s |
amount | mole | mol |
temperature | kelvin | K |
electrical current | ampere | amp |
luminous intensity | candela | cd |
The United States uses the English (sometimes called Imperial) system of units for many quantities. Inches, feet, miles, gallons, pounds, and so forth, are all units connected with the English system of units. There have been many mistakes due to the improper conversion of units between the SI and English systems.
The size of each base unit is defined by international convention. For example, the kilogram is defined as the quantity of mass of a special metal cylinder kept in a vault in France (Figure \(\PageIndex{1}\)). The other base units have similar definitions and standards. The sizes of the base units are not always convenient for all measurements. For example, a meter is a rather large unit for describing the width of something as narrow as human hair. Instead of reporting the diameter of hair as 0.00012 m or as 1.2 × 10−4 m using scientific notation as discussed in section 1.4, SI also provides a series of prefixes that can be attached to the units, creating units that are larger or smaller by powers of 10.
![1.8.jpg](https://chem.libretexts.org/@api/deki/files/200084/1.8.jpg?revision=1&size=bestfit&height=320)
Common prefixes and their multiplicative factors are listed in Table \(\PageIndex{2}\). (Perhaps you have already noticed that the base unit kilogram is a combination of a prefix, kilo- meaning 1,000 ×, and a unit of mass, the gram.) Some prefixes create a multiple of the original unit: 1 kilogram equals 1,000 grams, and 1 megameter equals 1,000,000 meters. Other prefixes create a fraction of the original unit. Thus, 1 centimeter equals 1/100 of a meter, 1 millimeter equals 1/1,000 of a meter, 1 microgram equals 1/1,000,000 of a gram, and so forth.
Prefix | Abbreviation | Multiplicative Factor | Multiplicative Factor in Scientific Notation |
---|---|---|---|
giga- | G | 1,000,000,000 × | 109 × |
mega- | M | 1,000,000 × | 106 × |
kilo- | k | 1,000 × | 103 × |
deca- | D | 10 × | 101 × |
deci- | d | 1/10 × | 10−1 × |
centi- | c | 1/100 × | 10−2 × |
milli- | m | 1/1,000 × | 10−3 × |
micro- | µ* | 1/1,000,000 × | 10−6 × |
nano- | n | 1/1,000,000,000 × | 10−9 × |
*The letter µ is the Greek lowercase letter for m and is called “mu,” which is pronounced “myoo.” |
Both SI units and prefixes have abbreviations, and the combination of a prefix abbreviation with a base unit abbreviation gives the abbreviation for the modified unit. For example, kg is the abbreviation for kilogram. We will be using these abbreviations throughout this book.
What is the difference between “mass” and “weight”?
The mass of a body is a measure of its inertial property or how much matter it contains. The weight of a body is a measure of the force exerted on it by gravity or the force needed to support it. Gravity on earth gives a body a downward acceleration of about 9.8 m/s2. In common parlance, weight is often used as a synonym for mass in weights and measures. For instance, the verb “to weigh” means “to determine the mass of” or “to have a mass of.” The incorrect use of weight in place of mass should be phased out, and the term mass used when mass is meant. The SI unit of mass is the kilogram (kg). In science and technology, the weight of a body in a particular reference frame is defined as the force that gives the body an acceleration equal to the local acceleration of free fall in that reference frame. Thus, the SI unit of the quantity weight defined in this way (force) is the newton (N).
Derived SI Units
Concept Review Exercises
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What is the difference between a base unit and a derived unit? Give two examples of each type of unit.
2. Do units follow the same mathematical rules as numbers do? Give an example to support your answer.
3. What is density?
Answers
-
Base units are the seven fundamental units of SI; derived units are constructed by making combinations of the base units; Two examples of base units: kilograms and meters (answers will vary); Two examples of derived units: grams per milliliter and joules (answers will vary).
2. yes; mL×gmL=gmL×gmL=g (answers will vary)
3. Density is defined as the mass of an object divided by its volume
Key Takeaways
- Recognize the SI base units and derived units.
- Combining prefixes with base units creates new units of larger or smaller sizes.
Exercises
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List four base units.
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List four derived units.
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How many meters are in 1 km? How many centimeters are in 1 m?
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How many grams are in 1 Mg? How many microliters are in 1 L?
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Complete the following table:
Unit Abbreviation centiliter ms cm kL micrometer -
Complete the following table:
Unit Abbreviation microliter kilosecond dL ns millimeter -
What are some appropriate units for density?
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A derived unit for velocity, which is the change of position with respect to time, is meters per second (m/s). Give three other derived units for velocity.
Answers
1. second, meter, kilogram, and kelvin (answers will vary)
2. square meter (m2), cubic meter (m3), grams per milliliter (g/mL), milliliters per second (mL/s) answers will vary
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1,000; 100
4. 1,000,000; 1,000,000
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Unit Abbreviation centiliter cL millisecond ms centimeter cm kiloliter kL micrometer µm
6.
Unit | Abbreviation |
---|---|
microliter | µL |
kilosecond | ks |
deciliter | dL |
nanosecond | ns |
millimeter | mm |
7. grams per liter, grams per milliliter, and kilograms per liter (answers will vary)
8. kilometers per hour; meters per minute; millimeters per second (answers will vary)