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 SYSTEM aka 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 hectodeca Base Units meter gram liter deci centimilli

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 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 VolumesStandard Volumes Larger Volumes Milliliters (mL) Liter (L) Kiloliter (kL) 1000 mL = 1 L 1000 L = 1 kL Mili- means Kilo- means 1000

Measuring Mass Using the Metric System Small MassStandard MassLarger Mass Milligrams (mg) Gram (g) Kilograms (kg) 1000 mg = 1 g 1000 g = 1 kg Mili- means 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 = meters –16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage: meters = 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 hectodeca Base Units meter gram liter deci centimilli

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 cm

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 kil o hectodeca meter liter gram deci centimilli ( 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 centimeters or 1.00 meter = 10.0 decimeters = 100. centimeters kilo hectodeca meter liter gram deci centimilli

Metric System Now let’s try our previous example from meters to kilometers: meters = decameters = hectometers = 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 hectodeca meter liter gram deci centimilli

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 hectodeca meter liter gram deci centimilli

PRACTICE PROBLEMS

Metric System Now let’s start from meters and convert to centimeters 5 meters = 500 centimeters kilo hectodeca meter liter gram deci centimilli kilo hectodeca meter liter gram deci centimilli Now let’s start from kilometers and convert to meters.3 kilometers = 300 meters