1. Home
  2. Fundamentals of mathematics
  3. Measurement and geometry
  4. The metric system of measurement

9.2 The metric system of measurement

<< Chapter < Page
  Fundamentals of mathematics   Page 1 / 1
Chapter >> Page >
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses the Metric System of measurement. By the end of the module students should be more familiar with some of the advantages of the base ten number system, know the prefixes of the metric measures, be familiar with the metric system of measurement and be able to convert from one unit of measure in the metric system to another unit of measure

Section overview

  • The Advantages of the Base Ten Number System
  • Prefixes
  • Conversion from One Unit to Another Unit
  • Conversion Table

The advantages of the base ten number system

The metric system of measurement takes advantage of our base ten number sys­tem. The advantage of the metric system over the United States system is that in the metric system it is possible to convert from one unit of measure to another simply by multiplying or dividing the given number by a power of 10. This means we can make a conversion simply by moving the decimal point to the right or the left.

Prefixes

Common units of measure in the metric system are the meter (for length), the liter (for volume), and the gram (for mass). To each of the units can be attached a prefix. The metric prefixes along with their meaning are listed below.

    Metric prefixes

  • thousand
  • tenth
  • hundred
  • hundredth
  • ten
  • thousandth

For example, if length is being measured,
1 kilometer is equivalent to 1000 meters.
1 centimeter is equivalent to one hundredth of a meter.
1 millimeter is equivalent to one thousandth of a meter.

Conversion from one unit to another unit

Let's note three characteristics of the metric system that occur in the metric table of measurements.

  1. In each category, the prefixes are the same.
  2. We can move from a larger to a smaller unit of measure by moving the decimal point to the right .
  3. We can move from a smaller to a larger unit of measure by moving the decimal point to the left .

The following table provides a summary of the relationship between the basic unit of measure (meter, gram, liter) and each prefix, and how many places the decimal point is moved and in what direction.

kilo hecto deka unit deci centi milli

Basic Unit to Prefix Move the Decimal Point
unit to deka 1 to 10 1 place to the left
unit to hector 1 to 100 2 places to the left
unit to kilo 1 to 1,000 3 places to the left
unit to deci 1 to 0.1 1 place to the right
unit to centi 1 to 0.01 2 places to the right
unit to milli 1 to 0.001 3 places to the right

Conversion table

Listed below, in the unit conversion table, are some of the common metric units of measure.

Unit Conversion Table
Length 1   kilometer  ( km ) = 1,000 meters  ( m ) size 12{1" kilometer " \( "km" \) ="1,000 meters " \( m \) } {} 1, 000 × 1 m size 12{1,"000" times 1" m"} {}
1   hectometer  ( hm ) = 100 meters size 12{1" hectometer " \( "hm" \) ="100 meters "} {} 100 × 1 m size 12{"100" times 1" m"} {}
1   dekameter  ( dam ) = 10 meters size 12{1" dekameter " \( "dam" \) ="10 meters"} {} 10 × 1 m size 12{"10" times 1" m"} {}
1 meter (m) 1 × 1 m size 12{1 times 1" m"} {}
1   decimeter  ( dm ) = 1 10   meter size 12{1" decimeter " \( "dm" \) = { {1} over {"10"} } " meter"} {} . 1 × 1 m size 12{ "." 1 times 1" m"} {}
1   centimeter  ( cm ) = 1 100   meter size 12{1" centimeter " \( "cm" \) = { {1} over {"100"} } " meter"} {} . 01 × 1 m size 12{ "." "01" times 1" m"} {}
1   millimeter  ( mm ) = 1 1,000   meter size 12{1" millimeter " \( "mm" \) = { {1} over {"1,000"} } " meter"} {} . 001 × 1 m size 12{ "." "001" times 1" m"} {}
Mass 1   kilogram   ( kg ) = 1,000 grams   ( g ) size 12{"1 kilogram " \( "kg" \) ="1,000 grams " \( g \) } {} 1, 000 × 1 g size 12{1,"000" times 1" g"} {}
1   hectogram  ( hg ) = 100 grams size 12{"1 hectogram " \( "hg" \) ="100 grams"} {} 100 × 1 g size 12{"100" times 1" g"} {}
1   dekagram   ( dag ) = 10 grams size 12{"1 dekagram " \( "dag" \) ="10 grams"} {} 10 × 1 g size 12{"10" times 1" g"} {}
1   gram   (g) 1 × 1 g size 12{1 times 1" g"} {}
1   decigram   ( dg ) = 1 10   gram size 12{"1 decigram " \( "dg" \) = { {1} over {"10"} } " gram"} {} . 1 × 1 g size 12{ "." 1 times 1" g"} {}
1   centigram   ( cg ) = 1 100   gram size 12{"1 centigram " \( "cg" \) = { {1} over {"100"} } " gram"} {} . 01 × 1 g size 12{ "." "01" times 1" g"} {}
1   milligram   ( mg ) = 1 1,000   gram size 12{"1 milligram " \( "mg" \) = { {1} over {"1,000"} } " gram"} {} . 001 × 1 g size 12{ "." "001" times 1" g"} {}
Volume 1   kiloliter   ( kL ) = 1, 000   liters   ( L ) size 12{"1 kiloliter " \( "kL" \) =1,"000"" liters " \( L \) } {} 1, 000 × 1 L size 12{1,"000" times 1" L"} {}
1   hectoliter   ( hL ) = 100   liters size 12{"1 hectoliter " \( "hL" \) ="100"" liters"} {} 100 × 1 L size 12{"100" times 1" L"} {}
1   dekaliter   ( daL ) = 10   liters size 12{"1 dekaliter " \( "daL" \) ="10"" liters"} {} 10 × 1 L size 12{"10" times 1" L"} {}
1 liter (L) 1 × 1 L size 12{1 times 1" L"} {}
1   deciliter   ( dL ) = 1 10   liter size 12{"1 deciliter " \( "dL" \) = { {1} over {"10"} } " liter"} {} . 1 × 1 L size 12{ "." 1 times 1" L"} {}
1   centiliter   ( cL ) = 1 100   liter size 12{"1 centiliter " \( "cL" \) = { {1} over {"100"} } " liter"} {} . 01 × 1 L size 12{ "." "01" times 1" L"} {}
1   milliliter   ( mL ) = 1 1, 000   liter size 12{"1 milliliter " \( "mL" \) = { {1} over {1,"000"} } " liter"} {} . 001 × 1 L size 12{ "." "001" times 1" L"} {}
Time Same as the United States system

Distinction between mass and weight

There is a distinction between mass and weight. The weight of a body is related to gravity whereas the mass of a body is not. For example, your weight on the earth is different than it is on the moon, but your mass is the same in both places. Mass is a measure of a body's resistance to motion. The more massive a body, the more resistant it is to motion. Also, more massive bodies weigh more than less massive bodies.

Converting metric units

To convert from one metric unit to another metric unit:

  1. Determine the location of the original number on the metric scale (pictured in each of the following examples).
  2. Move the decimal point of the original number in the same direction and same number of places as is necessary to move to the metric unit you wish to go to.

We can also convert from one metric unit to another using unit fractions. Both methods are shown in [link] of [link] .

Sample set a

Convert 3 kilograms to grams.

  1. 3 kg can be written as 3.0 kg. Then,

    A line with hash marks dividing the line into seven segments. The segments are labeled, from left to right, kg, hg, dag, g, dg, cg, and mg. Below kg, hg, dagga, and g are arrows pointing from each segment to the neighboring segment on the right. These arrows are labeled 1, 2, and 3, indicating the number of places to the right.

    3.0 kg is equal to 3000g. An arrow is drawn under the three zeros in 3000, counting three decimal places to the right.

    Thus, 3kg = 3,000 g size 12{"3kg"="3,000 g"} {} .

  2. We can also use unit fractions to make this conversion.

    Since we are converting to grams, and 1, 000     g = 1   kg size 12{1,"000"g="1kg"} {} , we choose the unit fraction 1,000   g 1   kg size 12{ { {"1,000 g"} over {"1 kg"} } } {} since grams is in the numerator.

    3   kg = 3 kg ⋅ 1,000   g 1 kg = 3   kg ⋅ 1,000   g 1   kg = 3 ⋅ 1,000   g = 3,000   g

Got questions? Get instant answers now!

Convert 67.2 hectoliters to milliliters.

A line with hash marks dividing the line into seven segments. The segments are labeled, from left to right, kL, hL, dal, L, dL, cL, and mL. Below hL, dal, L, dL, cL, and mL are arrows pointing from each segment to the neighboring segment on the right. These arrows are labeled 1 through 5 indicating the number of places to the right.

62.7 hL is equal to 6720000 mL. An arrow is drawn under the rightmost five digits in 6720000, counting five decimal places to the right.

Thus, 67 . 2 hL = 6,720,000 mL size 12{"67" "." "2 hL"="6,720,000 mL"} {} .

Got questions? Get instant answers now!

Convert 100.07 centimeters to meters.

A line with hash marks dividing the line into seven segments. The segments are labeled, from left to right, km, hm, dam, m, dm, cm, mm. Below cm, dm, and m are arrows pointing from each segment to the neighboring segment on the left. These arrows are labeled 1 and 2, indicating the number of places to the left.

100.07 cm equals 1.0007 m. Arrows under the two leftmost zeros are labeled 1 and 2, pointing to the left, indicating the number of decimal places moved.

Thus, 100 . 07 cm = 1 . 0007 m size 12{"100" "." "07 cm "=" 1" "." "0007 m"} {} .

Got questions? Get instant answers now!

Convert 0.16 milligrams to grams.

A line with hash marks dividing the line into seven segments. The segments are labeled, from left to right, kg, hg, dg, g, dg, cg, and mg. Below g, dg, cg, and mg are arrows pointing from each segment to the neighboring segment on the left. These arrows are labeled 1, 2, and 3, indicating the number of places to the left.

0.16mg equals 0.00016g. Underneath the rightmost three zeros are arrows pointing to the left, labeled 1, 2, and 3, indicating the movement of the decimal point.

Thus, 0 . 16   mg = 0 . 00016 g . size 12{0 "." "16"" mg "=" 0" "." "00016 g" "." } {}

Got questions? Get instant answers now!

Practice set a

Convert 411 kilograms to grams.

411,000 g

Got questions? Get instant answers now!

Convert 5.626 liters to centiliters.

562.6 cL

Got questions? Get instant answers now!

Convert 80 milliliters to kiloliters.

0.00008 kL

Got questions? Get instant answers now!

Convert 150 milligrams to centigrams.

15 cg

Got questions? Get instant answers now!

Convert 2.5 centimeters to meters.

0.025 m

Got questions? Get instant answers now!

Exercises

Make each conversion.

87 m to cm

8,700 cm

Got questions? Get instant answers now!

905 L to mL

Got questions? Get instant answers now!

16,005 mg to g

16.005 g

Got questions? Get instant answers now!

48.66 L to dL

Got questions? Get instant answers now!

11.161 kL to L

11,161 L

Got questions? Get instant answers now!

521.85 cm to mm

Got questions? Get instant answers now!

1.26 dag to dg

126 dg

Got questions? Get instant answers now!

99.04 dam to cm

Got questions? Get instant answers now!

0.51 kL to daL

5.1 daL

Got questions? Get instant answers now!

0.17 kL to daL

Got questions? Get instant answers now!

0.05 m to dm

0.5 dm

Got questions? Get instant answers now!

0.001 km to mm

Got questions? Get instant answers now!

8.106 hg to cg

81,060 cg

Got questions? Get instant answers now!

17.0186 kL to mL

Got questions? Get instant answers now!

3 cm to m

0.03 m

Got questions? Get instant answers now!

9 mm to m

Got questions? Get instant answers now!

4 g to mg

4,000 mg

Got questions? Get instant answers now!

2 L to kL

Got questions? Get instant answers now!

6 kg to mg

6,000,000 mg

Got questions? Get instant answers now!

7 daL to mL

Got questions? Get instant answers now!

Exercises for review

( [link] ) Find the value of 5 8 − 1 3 + 3 4 size 12{ { {5} over {8} } - { {1} over {3} } + { {3} over {4} } } {} .

25 24 = 1 1 24 size 12{ { {"25"} over {"24"} } =1 { {1} over {"24"} } } {}

Got questions? Get instant answers now!

( [link] ) Solve the proportion: 9 x = 27 60 size 12{ { {9} over {x} } = { {"27"} over {"60"} } } {} .

Got questions? Get instant answers now!

( [link] ) Use the method of rounding to estimate the sum: 8, 226 + 4, 118 size 12{8,"226"+4,"118"} {} .

12,300 (12,344)

Got questions? Get instant answers now!

( [link] ) Use the clustering method to estimate the sum: 87 + 121 + 118 + 91 + 92 size 12{"87"+"121"+"118"+"91"+"92"} {} .

Got questions? Get instant answers now!

( [link] ) Convert 3 in. to yd.

0 . 08 3 ¯ size 12{0 "." "08" {overline {3}} } {} yard

Got questions? Get instant answers now!

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask