Metric System
Jen Kershaw
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Printed: June 30, 2014
AUTHOR
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Metric System
1
Metric System
Here you’ll learn to identify equivalence among metric units of measure.
Karina’s seventh grade class is reading a book about Greek history. Karina is fascinated by the Greek Gods and with
all of the mythology surrounding them. The class has decided to focus on the sporting events of the Greek Gods
since often the stories of mythology are studied in fifth or sixth grade. Their teacher, Ms. Harris thinks this will be
a good focus for the class.
“The first javelin was thrown in 708 BC by Hercules, the son of Zeus,” Ms. Harris said at the beginning of class.
“The javelin was originally 2.3 to 2.4 meters long and weighed about 400 grams. Then later, the weight and length
of the javelin changed,” Ms. Harris stopped lecturing and began scanning through her notes.
“Hmmm.. I can’t seem to find the place where I wrote down the new dimensions of the javelin,” She said. “Alright,
that will be your homework. Also, figure out the difference between the javelin of the past and the present.”
Karina hurried out of the class and during study hall began scouring the library for information. She found a great
book on track and field and began reading all of the information.
She discovered that the new length of the javelin is 2.6 meters and is 800 grams in weight. Now she needs to figure
out the difference.
Measuring metrics and performing operations with metric measurements is what this Concept is all about. It
is perfect timing for Karina too. At the end of the Concept, you will be able to help her with her homework.
Guidance
Previously we worked with powers of 10. Let’s review some of the places where you have seen powers of ten.
Our place-value system—on both the left and right sides of the decimal point—is based on powers of 10. This
fact helps us manipulate numbers so they are easier to use in operations. When adding, we add tens to the left
place-value, and when subtracting we borrow tens and regroup them to the right place-value.
In dividing decimals, we multiply the divisor and dividend by 10 until the divisor is a whole number. In scientific
notation, we use powers of 10 to convert numbers to a simpler form.
This brings us to measurement and the metric system. The metric system of measurement is also based on
powers of 10.
The metric system includes units of length (meters), weight (grams), and volume (liter).
Look at the metric chart below to get an idea of the base-ten relationship among metric units. There are many
decimal places, but you will get an idea of which units of measure are larger and which are smaller. This will help
you as you learn about equivalence, or about determining which values are equal.
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Notice that the metric system has units of length, weight and volume. Our customary system does too, but
familiarizing yourself with the metric system is helpful especially when traveling or working in the sciences.
Metric Units of Length
millimeter (mm)
.1 cm
.001 m
.000001 km
centimeter (cm)
10 mm
.01 m
.00001 km
meter (m)
1000 mm
100 cm
.001 km
kilometer (km)
1, 000, 000 mm
100, 000 cm
1000 m
milligram (mg)
.1 cg
.001 g
.000001 kg
centigram (cg)
10 mg
.01 g
.00001 kg
gram (g)
1000 mg
100 cg
.001 kg
kilogram (kg)
1, 000, 000 mg
100, 000 cg
1000 g
milliliter (ml)
.1 cl
.001 l
.000001 kl
centiliter (cl)
10 ml
.01 l
.00001 kl
liter (l)
1000 ml
100 cl
.001 kl
kiloliter (kl)
1, 000, 000 ml
100, 000 cl
1000 l
Metric Units of Mass
Metric Units of Volume
You aren’t. Remember all of that isn’t realistic. However, you can learn the prefixes of each measurement
unit and that can help you in the long run.
milli - means one-thousandth;
centi - means one-hundredth,
kilo - means one thousand.
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Chapter 1. Metric System
Notice that the first two represent a decimal, you can tell because the “th” is used at the end of the definition.
The prefix kilo means one thousand and this is not in decimal form.
Now let’s look at some equivalent measures.
Write down these notes before continuing with the lesson.
How can we convert different units of measurement?
You can move back and forth among the metric units by multiplying or dividing by powers of 10.
To get from kilometers to meters, multiply by 1,000.
To get from meters to centimeters, multiply by 100.
To get from meters to millimeters, multiply by 1,000.
Working backwards, to get from kilometers to meters, divide by 1,000.
To get from meters to centimeters, divide by 100.
To get from meters to millimeters, divide by 1,000.
To get from kilometers to millimeters, divide by 1, 000, 000 (1, 000 × 1, 000)
Let’s look at how we can use this information.
Fill in the blanks with the equivalent measurement.
100 centiliter = ___ liter
10 centimeters = ___ meters
1 kilogram = ___ centigrams
1 milligram = ___ centigram
To figure these out, look back at the conversion chart and at the operations needed to convert one unit to
another. Whether you are multiplying or dividing, you will need the correct number to multiply or divide by.
There are 100 centiliters in 1 liter.
There are 100 centimeters in a meter. We divide by 100. 10 divided by 100 = .1
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10 centimeters = .1 meters
There are 1,000 kilograms in a gram. We multiply 1 × 1, 000 = 1, 000 grams; there are 100 centigrams in a gram;
1, 000 × 100 = 100, 000
1 kilogram = 100,000 centigrams
There are 10 milligrams in a centigram 1 ÷ 10 = .1
1 milligram = .1 centigram
Notice that when we go from a smaller unit to a larger unit, we divide. When we go from a larger unit to a
smaller unit we multiply.
Convert 23 kilograms into grams.
We start by noticing that we are going from a larger unit to a smaller unit. Therefore, we are going to multiply.
There are 100 grams in 1 kilogram. There are 23 kilograms in this problem.
23 × 1000 = 23, 000
23 kilograms = 23, 000 grams.
Convert the following units to their equivalent.
Example A
10 centigrams = _____ grams
Solution: .1 grams
Example B
1 meter = _____ millimeters
Solution: 1000 millimeters
Example C
15 kilometers = _____ meters
Solution: 15, 000 meters.
Now back to the javelin dimensions.
Reread the original problem. Then help Karina with her problem.
Karina’s seventh grade class is reading a book about Greek history. Karina is fascinated by the Greek Gods and with
all of the mythology surrounding them. The class has decided to focus on the sporting events of the Greek Gods
4
www.ck12.org
Chapter 1. Metric System
since often the stories of mythology are studied in fifth or sixth grade. Their teacher, Ms. Harris thinks this will be
a good focus for the class.
“The first javelin was thrown in 708 BC by Hercules, the son of Zeus,” Ms. Harris said at the beginning of class.
“The javelin was originally 2.3 to 2.4 meters long and weighed about 400 grams. Then later, the weight and length
of the javelin changed,” Ms. Harris stopped lecturing and began scanning through her notes.
“Hmmm.. I can’t seem to find the place where I wrote down the new dimensions of the javelin,” She said. “Alright,
that will be your homework. Also, figure out the difference between the javelin of the past and the present.”
Karina hurried out of the class and during study hall began scouring the library for information. She found a great
book on track and field and began reading all of the information.
She discovered that the new length of the javelin is 2.6 meters and is 800 grams in weight. Now she needs to figure
out the difference.
To figure out the difference, Karina needs to subtract the old length with the new length. The old length was
between 2.3 and 2.4. Karina decides to find the average of the range of numbers. To find the average, you add
the values and divide by the number of terms in the series
2.3 + 2.4 = 4.7 ÷ 2 = 2.35
Next, she subtracts 2.35 from the original javelin length.
2.6
−2.35
.25
There is a difference of
1
4
of a meter or .25 of a meter.
Next, we can figure the weight difference.
400 grams was the old weight and 800 grams is the new weight. The new weight of the javelin is twice the
weight of the old javelin.
Karina finishes her homework and makes a note of the fact that while the length of the javelin didn’t double
that the weight of it did!
Vocabulary
Equivalence
means equal.
Metric System
a system of measuring length, weight and volume
Milli
means
1
1000
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Centi
means
1
100
Kilo
means 1000
Measurement
comparing the quality of an object against a standard based on what you are measuring.
Guided Practice
Here is one for you to try on your own.
Convert 25,000 meters into kilometers.
Answer
First, notice that we are going from a larger unit to a smaller unit, so we need to divide.
There are 1000 meters in 1 kilometer.
25, 000 ÷ 1000 = 25
25, 000 meters = 25 kilometers
This is our answer.
Video Review
MEDIA
Click image to the left for more content.
This is a James Sousa video on metric system conversions and equivalence.
Practice
Directions: Fill in the blanks with the equivalent measurement.
1. 1,000 centimeters = ___ meters
2. 10 kiloliters = ___ centiliters
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Chapter 1. Metric System
3. 1,000 milligrams = ___ centigrams
4. 100 milliliters = ___ centiliters
Directions: Fill in the blanks with the equivalent measurement.
5. 200 milligrams = ___ kilograms
6. 20 centimeters = ___ meters
7. 2 liters = ___ kiloliters
8. 2,000 centigrams = ___ kilograms
Directions: Fill in the blanks with the equivalent measurements for 180.76 centimeters.
9. ___ meters
10. ___ millimeters
11. ___ kilometers
Directions: Fill in the blanks with the equivalent measurements for 0.4909 kiloliters.
12. ___ liters
13. ___ centiliters
14. ___ milliliters
15. How many liters in one kiloliter?
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