Connexions

You are here: Home » Content » Measurement and Geometry: The Metric System of Measurement

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

Endorsed by (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
• CCQ

This module is included in aLens by: Community College of QatarAs a part of collection: "Fundamentals of Mathematics"

"Used as supplemental materials for developmental math courses."

Click the "CCQ" link to see all content they endorse.

Click the tag icon to display tags associated with this content.

• College Open Textbooks

This module is included inLens: Community College Open Textbook Collaborative
By: CC Open Textbook CollaborativeAs a part of collection: "Fundamentals of Mathematics"

"Reviewer's Comments: 'I would recommend this text for a basic math course for students moving on to elementary algebra. The information in most chapters is useful, very clear, and easily […]"

Click the "College Open Textbooks" link to see all content they endorse.

Click the tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
• Featured Content

This module is included inLens: Connexions Featured Content
By: ConnexionsAs a part of collection: "Fundamentals of Mathematics"

"Fundamentals of Mathematics is a work text that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and […]"

Click the "Featured Content" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

Also in these lenses

• UniqU content

This module is included inLens: UniqU's lens
By: UniqU, LLCAs a part of collection: "Fundamentals of Mathematics"

Click the "UniqU content" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Measurement and Geometry: The Metric System of Measurement

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: 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

• kilo — thousand
• deci — tenth
• hecto — hundred
• centi — hundredth
• deka — ten
• milli — 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 ) 1   kilometer  ( km ) = 1,000 meters  ( m ) size 12{1" kilometer " $$"km"$$ ="1,000 meters " $$m$$ } {} 1, 000 × 1 m 1, 000 × 1 m size 12{1,"000" times 1" m"} {} 1   hectometer  ( hm ) = 100 meters 1   hectometer  ( hm ) = 100 meters size 12{1" hectometer " $$"hm"$$ ="100 meters "} {} 100 × 1 m 100 × 1 m size 12{"100" times 1" m"} {} 1   dekameter  ( dam ) = 10 meters 1   dekameter  ( dam ) = 10 meters size 12{1" dekameter " $$"dam"$$ ="10 meters"} {} 10 × 1 m 10 × 1 m size 12{"10" times 1" m"} {} 1 meter (m) 1 × 1 m 1 × 1 m size 12{1 times 1" m"} {} 1   decimeter  ( dm ) = 1 10   meter 1   decimeter  ( dm ) = 1 10   meter size 12{1" decimeter " $$"dm"$$ = { {1} over {"10"} } " meter"} {} . 1 × 1 m . 1 × 1 m size 12{ "." 1 times 1" m"} {} 1   centimeter  ( cm ) = 1 100   meter 1   centimeter  ( cm ) = 1 100   meter size 12{1" centimeter " $$"cm"$$ = { {1} over {"100"} } " meter"} {} . 01 × 1 m . 01 × 1 m size 12{ "." "01" times 1" m"} {} 1   millimeter  ( mm ) = 1 1,000   meter 1   millimeter  ( mm ) = 1 1,000   meter size 12{1" millimeter " $$"mm"$$ = { {1} over {"1,000"} } " meter"} {} . 001 × 1 m . 001 × 1 m size 12{ "." "001" times 1" m"} {} Mass 1   kilogram   ( kg ) = 1,000 grams   ( g ) 1   kilogram   ( kg ) = 1,000 grams   ( g ) size 12{"1 kilogram " $$"kg"$$ ="1,000 grams " $$g$$ } {} 1, 000 × 1 g 1, 000 × 1 g size 12{1,"000" times 1" g"} {} 1   hectogram  ( hg ) = 100 grams 1   hectogram  ( hg ) = 100 grams size 12{"1 hectogram " $$"hg"$$ ="100 grams"} {} 100 × 1 g 100 × 1 g size 12{"100" times 1" g"} {} 1   dekagram   ( dag ) = 10 grams 1   dekagram   ( dag ) = 10 grams size 12{"1 dekagram " $$"dag"$$ ="10 grams"} {} 10 × 1 g 10 × 1 g size 12{"10" times 1" g"} {} 1   gram   (g) 1 × 1 g 1 × 1 g size 12{1 times 1" g"} {} 1   decigram   ( dg ) = 1 10   gram 1   decigram   ( dg ) = 1 10   gram size 12{"1 decigram " $$"dg"$$ = { {1} over {"10"} } " gram"} {} . 1 × 1 g . 1 × 1 g size 12{ "." 1 times 1" g"} {} 1   centigram   ( cg ) = 1 100   gram 1   centigram   ( cg ) = 1 100   gram size 12{"1 centigram " $$"cg"$$ = { {1} over {"100"} } " gram"} {} . 01 × 1 g . 01 × 1 g size 12{ "." "01" times 1" g"} {} 1   milligram   ( mg ) = 1 1,000   gram 1   milligram   ( mg ) = 1 1,000   gram size 12{"1 milligram " $$"mg"$$ = { {1} over {"1,000"} } " gram"} {} . 001 × 1 g . 001 × 1 g size 12{ "." "001" times 1" g"} {} Volume 1   kiloliter   ( kL ) = 1, 000   liters   ( L ) 1   kiloliter   ( kL ) = 1, 000   liters   ( L ) size 12{"1 kiloliter " $$"kL"$$ =1,"000"" liters " $$L$$ } {} 1, 000 × 1 L 1, 000 × 1 L size 12{1,"000" times 1" L"} {} 1   hectoliter   ( hL ) = 100   liters 1   hectoliter   ( hL ) = 100   liters size 12{"1 hectoliter " $$"hL"$$ ="100"" liters"} {} 100 × 1 L 100 × 1 L size 12{"100" times 1" L"} {} 1   dekaliter   ( daL ) = 10   liters 1   dekaliter   ( daL ) = 10   liters size 12{"1 dekaliter " $$"daL"$$ ="10"" liters"} {} 10 × 1 L 10 × 1 L size 12{"10" times 1" L"} {} 1 liter (L) 1 × 1 L 1 × 1 L size 12{1 times 1" L"} {} 1   deciliter   ( dL ) = 1 10   liter 1   deciliter   ( dL ) = 1 10   liter size 12{"1 deciliter " $$"dL"$$ = { {1} over {"10"} } " liter"} {} . 1 × 1 L . 1 × 1 L size 12{ "." 1 times 1" L"} {} 1   centiliter   ( cL ) = 1 100   liter 1   centiliter   ( cL ) = 1 100   liter size 12{"1 centiliter " $$"cL"$$ = { {1} over {"100"} } " liter"} {} . 01 × 1 L . 01 × 1 L size 12{ "." "01" times 1" L"} {} 1   milliliter   ( mL ) = 1 1, 000   liter 1   milliliter   ( mL ) = 1 1, 000   liter size 12{"1 milliliter " $$"mL"$$ = { {1} over {1,"000"} } " liter"} {} . 001 × 1 L . 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 Example 1 of Section 6.

Sample Set A

Example 1

Convert 3 kilograms to grams.

1. (a) 3 kg can be written as 3.0 kg. Then,

Thus, 3kg=3,000 g3kg=3,000 g size 12{"3kg"="3,000 g"} {}.

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

Since we are converting to grams, and 1,000    g=1   kg1,000    g=1   kg size 12{1,"000"g="1kg"} {}, we choose the unit fraction 1,000   g1   kg1,000   g1   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 3   kg = 3 kg 1,000   g 1 kg = 3   kg 1,000   g 1   kg = 3 1,000   g = 3,000   g

Example 2

Convert 67.2 hectoliters to milliliters.

Thus, 67.2 hL=6,720,000 mL67.2 hL=6,720,000 mL size 12{"67" "." "2 hL"="6,720,000 mL"} {}.

Example 3

Convert 100.07 centimeters to meters.

Thus, 100.07 cm = 1.0007 m100.07 cm = 1.0007 m size 12{"100" "." "07 cm "=" 1" "." "0007 m"} {}.

Example 4

Convert 0.16 milligrams to grams.

Thus, 0.16   mg = 0.00016 g.0.16   mg = 0.00016 g. size 12{0 "." "16"" mg "=" 0" "." "00016 g" "." } {}

Practice Set A

Exercise 1

Convert 411 kilograms to grams.

411,000 g

Exercise 2

Convert 5.626 liters to centiliters.

562.6 cL

Exercise 3

Convert 80 milliliters to kiloliters.

0.00008 kL

Exercise 4

Convert 150 milligrams to centigrams.

15 cg

Exercise 5

Convert 2.5 centimeters to meters.

0.025 m

Exercises

Make each conversion.

87 m to cm

8,700 cm

905 L to mL

16,005 mg to g

16.005 g

48.66 L to dL

11.161 kL to L

11,161 L

521.85 cm to mm

1.26 dag to dg

126 dg

99.04 dam to cm

0.51 kL to daL

5.1 daL

0.17 kL to daL

0.05 m to dm

0.5 dm

0.001 km to mm

8.106 hg to cg

81,060 cg

17.0186 kL to mL

3 cm to m

0.03 m

9 mm to m

4 g to mg

4,000 mg

2 L to kL

6 kg to mg

6,000,000 mg

7 daL to mL

Exercises for Review

Exercise 26

((Reference)) Find the value of 5813+345813+34 size 12{ { {5} over {8} } - { {1} over {3} } + { {3} over {4} } } {}.

Solution

2524=11242524=1124 size 12{ { {"25"} over {"24"} } =1 { {1} over {"24"} } } {}

Exercise 27

((Reference)) Solve the proportion: 9x=27609x=2760 size 12{ { {9} over {x} } = { {"27"} over {"60"} } } {}.

Exercise 28

((Reference)) Use the method of rounding to estimate the sum: 8,226+4,1188,226+4,118 size 12{8,"226"+4,"118"} {}.

12,300 (12,344)

Exercise 29

((Reference)) Use the clustering method to estimate the sum: 87+121+118+91+9287+121+118+91+92 size 12{"87"+"121"+"118"+"91"+"92"} {}.

Exercise 30

((Reference)) Convert 3 in. to yd.

Solution

0.083¯0.083¯ size 12{0 "." "08" {overline {3}} } {} yard

Content actions

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks