1.14: The Metric System
- Page ID
- 153118
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You will NOT need a calculator for this module.
The metric system was first implemented following the French Revolution; if we’re overthrowing the monarchy, why should we use a unit of a “foot” that is based on the length of a king’s foot?
The metric system was designed to be based on the natural world, and different units are related to each other by powers of \(10\) instead of weird numbers like \(3\), \(12\), \(16\), and \(5,280\)… This makes converting between metric units incredibly easy because all we need to do is move the decimal point.
The table below shows the most common metric prefixes. The prefixes are arranged in order so that we can convert between them simply by moving the decimal point the same number of places shown in the table.
| kilo- (k) | hecta- (h) | deka- (da) | [base unit] | deci- (d) | centi- (c) | milli- (m) |
|---|---|---|---|---|---|---|
| \(1,000\) | \(100\) | \(10\) | \(1\) | \(0.1\) | \(0.01\) | \(0.001\) |
| \(1,000\) | \(100\) | \(10\) | \(1\) | \(\dfrac{1}{10}\) | \(\dfrac{1}{100}\) | \(\dfrac{1}{1,000}\) |
| \(10^{3}\) | \(10^{2}\) | \(10^{1}\) | \(10^{0}\) | \(10^{-1}\) | \(10^{-2}\) | \(10^{-3}\) |
Because deka- and deci- both start with d, the abbreviation for deka- is da.
Metric System: Measurements of Length
The base unit of length is the meter, which is a bit longer than a yard (three feet). Because the prefix kilo- means one thousand, \(1\) kilometer is \(1,000\) meters. (One kilometer is around six tenths of a mile.) Similarly, because the prefix centi- means one hundredth, \(1\) centimeter is \(\dfrac{1}{100}\) of a meter, or \(1\) meter is \(100\) centimeters. (One centimeter is roughly the thickness of a pen.) And because the prefix milli- means one thousandth, \(1\) millimeter is \(\dfrac{1}{1,000}\) of a meter, or \(1\) meter is \(1,000\) millimeters. (One millimeter is roughly the thickness of a credit card.)
From each of the four choices, choose the most reasonable measure.
- The length of a car:
\(5\) kilometers, \(5\) meters, \(5\) centimeters, \(5\) millimeters - The height of a notebook:
\(28\) kilometers, \(28\) meters, \(28\) centimeters, \(28\) millimeters - The distance to the next town:
\(3.8\) kilometers, \(3.8\) meters, \(3.8\) centimeters, \(3.8\) millimeters - An adult woman’s height:
\(1.6\) kilometers, \(1.6\) meters, \(1.6\) centimeters, \(1.6\) millimeters - An adult woman’s height:
\(160\) kilometers, \(160\) meters, \(160\) centimeters, \(160\) millimeters - The thickness of a pane of glass:
\(3\) kilometers, \(3\) meters, \(3\) centimeters, \(3\) millimeters
| kilo- (km) | hecta- (hm) | deka- (dam) | meter (m) | deci- (dm) | centi- (cm) | milli- (mm) |
|---|---|---|---|---|---|---|
| \(1,000\) | \(100\) | \(10\) | \(1\) | \(0.1\) | \(0.01\) | \(0.001\) |
| \(1,000\) | \(100\) | \(10\) | \(1\) | \(\dfrac{1}{10}\) | \(\dfrac{1}{100}\) | \(\dfrac{1}{1,000}\) |
| \(10^{3}\) | \(10^{2}\) | \(10^{1}\) | \(10^{0}\) | \(10^{-1}\) | \(10^{-2}\) | \(10^{-3}\) |
To convert metric units, you can simply move the decimal point left or right the number of places indicated in the table above. No calculator required!
A 2024 Chevrolet Silverado 1500 pickup truck is \(5.36\) meters long.[1]
- Convert \(5.36\) meters to centimeters.
- Convert \(5.36\) meters to millimeters.
One mile is approximately 1.609 kilometers.
- Convert \(1.609\) kilometers to meters.
- Convert \(1.609\) kilometers to centimeters.
A sheet of A4 paper[2] is 297 millimeters long.
- Convert \(297\) millimeters to meters.
- Convert \(297\) millimeters to centimeters.
The Burj Khalifa in Dubai is the world’s tallest building, with a height of 828 meters.[3]
- Convert \(828\) meters to kilometers.
- Convert \(828\) meters to dekameters.
Metric System: Measurements of Weight or Mass
The base unit for mass is the gram, which is about the mass of a paper clip. A kilogram is \(1,000\) grams; as we’ll see in the next module, this is around \(2.2\) pounds. The active ingredients in medicines may be measured using the milligram.
From each of the three choices, choose the most reasonable measure.
- The mass of an apple:
\(100\) kilograms, \(100\) grams, \(100\) milligrams - The mass of an adult man:
\(80\) kilograms, \(80\) grams, \(80\) milligrams - The amount of active ingredient in a pain relief pill:
\(500\) kilograms, \(500\) grams, \(500\) milligrams - The base vehicle weight of a Chevrolet Silverado 1500 pickup truck:
\(2,000\) kilograms, \(2,000\) grams, \(2,000\) milligrams
| kilo- (kg) | hecta- (hg) | deka- (dag) | gram (g) | deci- (dg) | centi- (cg) | milli- (mg) |
|---|---|---|---|---|---|---|
| \(1,000\) | \(100\) | \(10\) | \(1\) | \(0.1\) | \(0.01\) | \(0.001\) |
| \(1,000\) | \(100\) | \(10\) | \(1\) | \(\dfrac{1}{10}\) | \(\dfrac{1}{100}\) | \(\dfrac{1}{1,000}\) |
| \(10^{3}\) | \(10^{2}\) | \(10^{1}\) | \(10^{0}\) | \(10^{-1}\) | \(10^{-2}\) | \(10^{-3}\) |
This table is identical to the previous table; the only difference is that the base unit “meter” has been replaced by “gram”. This means that converting metric units of mass is exactly the same process as converting metric units of length.
A five-pound bag of flour weighs about \(2.27\) kilograms.
- Convert \(2.27\) kilograms to grams.
- Convert \(2.27\) kilograms to milligrams.
A 20-ounce bottle of Dr. Pepper contains \(65\) grams of sugars.
- Convert \(65\) grams to centigrams.
- Convert \(65\) grams to milligrams.
- Convert \(65\) grams to kilograms.
A 20-ounce bottle of Dr. Pepper contains \(95\) milligrams of sodium.
- Convert \(95\) milligrams to centigrams.
- Convert \(95\) milligrams to grams.
Metric System: Measurements of Volume or Capacity
The base unit of volume is the liter, which is slightly larger than one quart. The milliliter is also commonly used; of course, there are \(1,000\) milliliters in \(1\) liter.
In case you were wondering, the units of volume, length, and mass are all connected; one cubic centimeter (a cube with each side equal to \(1\) cm) has the same volume as one milliliter, and one milliliter of water has a mass of one gram.
From each of the two choices, choose the more reasonable measure.
- The capacity of a car’s gas tank: \(50\) liters, \(50\) milliliters
- A dosage of liquid cough medicine: \(30\) liters, \(30\) milliliters
| kilo- (kL) | hecta- (hL) | deka- (daL) | liter (L) | deci- (dL) | centi- (cL) | milli- (mL) |
|---|---|---|---|---|---|---|
| \(1,000\) | \(100\) | \(10\) | \(1\) | \(0.1\) | \(0.01\) | \(0.001\) |
| \(1,000\) | \(100\) | \(10\) | \(1\) | \(\dfrac{1}{10}\) | \(\dfrac{1}{100}\) | \(\dfrac{1}{1,000}\) |
| \(10^{3}\) | \(10^{2}\) | \(10^{1}\) | \(10^{0}\) | \(10^{-1}\) | \(10^{-2}\) | \(10^{-3}\) |
Again, this table is identical to the previous tables; just move the decimal point left or right to convert the units.
- A bottle of sparkling water is labeled 50 cl. Convert 50 centiliters to liters.
- A “1-liter” bag of saline solution for intravenous use actually contains about 1.05 liters of solution.[4] How many deciliters is this?
- A carton of orange juice has a volume of 1.75 liters. Convert this into mL.
- One cup (8 fluid ounces) is approximately 250 milliliters. Convert 250 milliliters into liters.
- While being served drinks on IcelandAir, you notice that one mini bottle is labeled 50 mL, but another mini bottle is labeled 5 cL. How do the two bottles compare in size?
- The engine displacement of a Yamaha Majesty scooter is 125 cc (cubic centimeters), and the engine displacement of a Chevrolet Spark automobile is 1.4 L (liters). What is the approximate ratio of these engine displacements?
- How many 500-milliliter bottles of Coke are equivalent to one 2-liter bottle?
- Source: www.caranddriver.com/chevrolet/silverado-1500/specs↵
- A4 is a bit narrower and a bit longer than standard letter paper that we use in the U.S. and Canada. ↵
- Source: en.Wikipedia.org/wiki/Burj_Khalifa↵
- Source: https://pubmed.ncbi.nlm.nih.gov/11096388/↵