The Metric System

In ancient times, there was confusion about how to measure

things.

When people tried to measure using the parts of their body they discovered that

people aren’t built the same. Not everyone has the same foot size, arm size, hand size,

etc.

To measure weight people tried using stones.

But what problem does this pose?

Stones come in different sizes.

And the same confusion arose when trying to find the volume of a container.

How many seeds does this container hold?

Again, it depends on the size of the seed.

Eventually people began to use the same ruler. Now a foot was a foot whether you lived in Eastonesia or

Westlovakia.

Above is a sample of the ruler we use today in the US, we use units like inches, feet, yards and miles for measuring length and distance.

To measure weight people started using a system of pounds, ounces,

and tons

and for Volume… Cups, Pints, Quarts and Gallons were used.

But this system, called the Customary System, was still

confusing (to everyone but the United States)

Because we are one of the only countries to still use the

Customary System of Measurement.

So if the United States is the only country still using the Customary

System to measure, what is everybody else using?

THE METRIC SYSTEMaka The International System of Units (SI)

• The metric system is based on a base unit that corresponds to a certain kind of measurement

• Length = meter

• Volume = liter

• Mass = gram

• Prefixes plus base units make up the metric system – Example:

• Centi + meter = Centimeter• Kilo + liter = Kiloliter

Metric System

• The three prefixes that we will use the most are:– Kilo (means 1000)– centi (means 1/100)– milli (means 1/1000)

kilo hecto deca

Base Units

meter

gram

liter

deci centi milli

Let me try to clear this up with a table:

Measuring Distances and Lengths Using the Metric System

Small Distances/Lengths

Standard Distances/Lengths

Larger Distances/Lengths

Millimeters (mm)

Centimeters (cm)

Meter (m)Kilometers (km)

Mili- means 1

1000

Kilo- means 1000

Let’s look at a Meter Stick

The space marked off is equal to 1 cm

This tiny space marked off is 1 mm

The height of our door is

about 2 meters.

So let’s add to our notes:

100 cm = 1 m

1,000 mm = 1 m

1,000 m = 1 km

Measuring Volume Using the Metric System

Small Volumes Standard Volumes

Larger Volumes

Milliliters (mL)Liter (L)

Kiloliter (kL)

1000 mL = 1 L

1000 L = 1 kL

Mili- means 1

1000

Kilo- means 1000

Measuring Mass Using the Metric System

Small Mass Standard Mass Larger Mass

Milligrams (mg)Gram (g)

Kilograms (kg)1000 mg = 1 g

1000 g = 1 kg

Mili- means 1

1000

Kilo- means 1000

Since there are currently two systems of measuring this can add

to the confusion…And sometimes misunderstandings about

measurements can lead to DISASTER!

The engineers and operators who worked on a multimillion dollar spacecraft made such a mistake. Some of them used feet and miles, while others used meters and kilometers…After blastoff the spacecraft

was supposed to orbit Mars, but instead it was lost in space forever.

However, even though the metric system has not been adopted by

people in the US, most Americans use it everyday.

Check your refrigerators, pantries, medicine cabinets and bathrooms.

Measured in grams

Measured in milligrams

Measured in milliliters

Many manufacturers use metric units because they are understood

all over the world.

• What if you need to measure a longer distance, like from your house to school?– Let’s say you live approximately 10 miles

from school• 10 miles = 16093 meters

– 16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage:

• 16093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place)

Metric System• These prefixes are based on powers of 10.

What does this mean?– From each prefix every “step” is either:

• 10 times larger or

• 10 times smaller

– For example• Centimeters are 10 times larger than millimeters• 1 centimeter = 10 millimeters

kilo hecto deca

Base Units

meter

gram

liter

deci centi milli

Metric System

– Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length

1 centimeter = 10 millimeters

Example not to scale

1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm

1 cm

40

41

41

40

Metric System• For each “step” to right,

you are multiplying by 10

• For example, let’s go from a base unit to centi

1 liter = 10 deciliters = 100 centiliters

2 grams = 20 decigrams = 200 centigrams

kilo hecto deca

meter

liter

gram

deci centi milli

( 1 x 10 = 10) = (10 x 10 = 100)

(2 x 10 = 20) = (20 x 10 = 200)

Metric System• An easy way to move within the metric system is

by moving the decimal point one place for each “step” desired

Example: change meters to centimeters

1 meter = 10 decimeters = 100 centimetersor

1.00 meter = 10.0 decimeters = 100. centimeters

kilo hecto deca

meter

liter

gram

deci centi milli

Metric System• Now let’s try our previous example from meters to

kilometers:

16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093 kilometers

• So for every “step” from the base unit to kilo, we moved the decimal 1 place to the left (the same direction as in the diagram below)

kilo hecto deca

meter

liter

gram

deci centi milli

Metric System

• If you move to the left in the diagram, move the decimal to the left

• If you move to the right in the diagram, move the decimal to the right

kilo hecto deca

meter

liter

gram

deci centi milli

• PRACTICE PROBLEMS

Metric System• Now let’s start from meters and convert to centimeters

5 meters = 500 centimeters

kilo hecto deca

meter

liter

gram

deci centi milli

kilo hecto deca

meter

liter

gram

deci centi milli

• Now let’s start from kilometers and convert to meters

.3 kilometers = 300 meters