Metric System

A prefixes plus a base unit makes up the metric system The metric system is based on a base unit that corresponds to a certain kind of measurement Base unit for length = meter Base unit for volume = liter Base unit for mass = gram A prefixes plus a base unit makes up the metric system Metric prefixes: Example: Centi + meter = Centimeter Kilo + liter = Kiloliter

The three prefixes that we will use the most are: kilo centi milli kilo- hecto- deca- Base Unit Meter Gram Liter deci- ceni- milli-

If you needed to measure length you would choose meter as your base unit Length of a tree branch 1.5 meters Length of a room 5 meters Length of a ball of twine stretched out 25 meters

But 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 = 16,093 meters 16,093 is a big number, what if we could convert it to a more manageable number? 16,093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place)

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 This is 10 times larger than this

millimeters Centimeters are 10 times larger than millimeters so it takes 10 millimeters to equal the same distance as 1 centimeter centimeter

For each “step” to the right, you are multiplying by 10 For example, let’s go from the base unit liters to centiliters Centi is 2 steps to the right of our base unit. If we have 1 liter of soda and want to know how many centiliters it is we have to do a little conversion. 1 liter x 10 x 10 = 100 centiliters (10 x 10 because centi is 2 steps away and each step to the right means you multiply by 10.

Another way to move within the metric system is by moving the decimal point one place for each “step” desired Example: convert 1 meter to centimeters 1 meter = 10 decimeters = 100 centimeters or 1.00 meter = 10.0 decimeters = 100. centimeters

Now let’s try moving left. Lets look at our example of living 16,093 meters from school and change it from meters to kilometers: Since we are moving left we need to divide by 10 for each step we take. 16,093 meters ÷ 10 = 1,609.3 decameters ÷ 10 = 160.93 hectometers ÷ 10 = 16.093 kilometers

Or we could move our decimal the correct number of place values to the left. 16,093 meters = 1,609.3 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)

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

Lets convert from centimeters to kilometers 400,000 centimeters = ? Kilometers Kilometers is 5 steps to the left. You can either divide by 10 five times or move the decimal point 5 place values to the left. Either way you will get the same answer. 400,000 centimeters = 4 kilometers

Practice 3 meters = ______ centimeters .4 liters = ______ deciliters 600 milligrams = _______ grams 5 kilometers = __________ hectometers 70 centimeters = _________ meters 900 deciliters= _______ milliliters A python caught in Florida measured 600 centimeters long. How many meters long was the snake? Faith weighed 5 kilograms at birth. How many grams did she weigh?