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14 The Metric System

Decorative image of Icelandic road signs

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 \frac{1}{10} \frac{1}{100} \frac{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 \frac{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 \frac{1}{1,000} of a meter, or 1 meter is 1,000 millimeters. (One millimeter is roughly the thickness of a credit card.)

Exercises

From each of the four choices, choose the most reasonable measure.

  1. The length of a car:
    5 kilometers, 5 meters, 5 centimeters, 5 millimeters
  2. The height of a notebook:
    28 kilometers, 28 meters, 28 centimeters, 28 millimeters
  3. The distance to the next town:
    3.8 kilometers, 3.8 meters, 3.8 centimeters, 3.8 millimeters
  4. An adult woman’s height:
    1.6 kilometers, 1.6 meters, 1.6 centimeters, 1.6 millimeters
  5. An adult woman’s height:
    160 kilometers, 160 meters, 160 centimeters, 160 millimeters
  6. 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 \frac{1}{10} \frac{1}{100} \frac{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!

Exercises

A 2024 Chevrolet Silverado 1500 pickup truck is 5.36 meters long.[1]

  1. Convert 5.36 meters to centimeters.
  2. Convert 5.36 meters to millimeters.

One mile is approximately 1.609 kilometers.

  1. Convert 1.609 kilometers to meters.
  2. Convert 1.609 kilometers to centimeters.

A sheet of A4 paper[2] is 297 millimeters long.

  1. Convert 297 millimeters to meters.
  2. Convert 297 millimeters to centimeters.

The Burj Khalifa in Dubai is the world’s tallest building, with a height of 828 meters.[3]

  1. Convert 828 meters to kilometers.
  2. 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.

Exercises

From each of the three choices, choose the most reasonable measure.

  1. The mass of an apple:
    100 kilograms, 100 grams, 100 milligrams
  2. The mass of an adult man:
    80 kilograms, 80 grams, 80 milligrams
  3. The amount of active ingredient in a pain relief pill:
    500 kilograms, 500 grams, 500 milligrams
  4. 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 \frac{1}{10} \frac{1}{100} \frac{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.

Exercises

A five-pound bag of flour weighs about 2.27 kilograms.

  1. Convert 2.27 kilograms to grams.
  2. Convert 2.27 kilograms to milligrams.

A 20-ounce bottle of Dr. Pepper contains 65 grams of sugars.

  1. Convert 65 grams to centigrams.
  2. Convert 65 grams to milligrams.
  3. Convert 65 grams to kilograms.

A 20-ounce bottle of Dr. Pepper contains 95 milligrams of sodium.

  1. Convert 95 milligrams to centigrams.
  2. 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.

1 liter is equivalent to a cube with sides of 10 centimeters. Image adapted by Cristianrodenas on Wikimedia Commons.

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.

illustration of one cubic centimeter of water on a scale showing a mass of 1 gram
Image by nclm on Wikimedia Commons.

Exercises

From each of the two choices, choose the more reasonable measure.

  1. The capacity of a car’s gas tank: 50 liters, 50 milliliters
  2. 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 \frac{1}{10} \frac{1}{100} \frac{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.

Exercises

  1. A bottle of sparkling water is labeled 50 cl. Convert 50 centiliters to liters.
  2. A “1-liter” bag of saline solution for intravenous use actually contains about 1.05 liters of solution.[4] How many deciliters is this?
  3. A carton of orange juice has a volume of 1.75 liters. Convert this into mL.
  4. One cup (8 fluid ounces) is approximately 250 milliliters. Convert 250 milliliters into liters.
  5. 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?
  6. 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?
  7. How many 500-milliliter bottles of Coke are equivalent to one 2-liter bottle?

Exercise Answers

  1. Source: https://www.caranddriver.com/chevrolet/silverado-1500/specs ↵
  2. A4 is a bit narrower and a bit longer than standard letter paper that we use in the U.S. and Canada. ↵
  3. Source: https://en.wikipedia.org/wiki/Burj_Khalifa ↵
  4. Source: https://pubmed.ncbi.nlm.nih.gov/11096388/ ↵

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Technical Mathematics, 2nd Edition Copyright © 2024 by Morgan Chase is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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