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Metric System Basics

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**Before we began, lets do some mental math. YAY!**

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**Don’t reach for that calculator!!!**

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Let’s begin!

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**Multiply each of the following numbers by 10**

27 x 10 = 157 x 10 = 56.4 x 10 = x 10 = x 10 = 270 1570 564 4588.7 235.16

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**Multiply each of the following numbers by 100**

22 x 100 = 156 x 100 = 45.1 x 100 = 74.32 x 100 = 3.567 x 100 = 2200 15600 4510 7432 356.7

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**Divide each of the following numbers by 10**

33.0 or 33 760.0 or 760 26.81 0.178 1.8395 330 10 = 7600 10 = 10 = 1.78 10 = 10 =

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**Divide each of the following numbers by 100**

2.10 or 2.1 78.00 or 78 4.216 0.821 210 100 = 7800 100 = 100 = 82.1 100 = 100 =

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Guess What! If you were able to do all that without a calculator, you can do metrics.

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Metric System The metric system is based on a base unit that corresponds to a certain kind of measurement Length = meter (m) Volume = liter (L or l) Weight (Mass) = gram (g) Prefixes added to the base units make up the metric system Example: Centi + meter = Centimeter = cm Kilo + liter = Kiloliter = kL or kl

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Common Prefixes The three prefixes that we will use the most in class are: kilo centi milli kilo hecto deca Base Units meter gram liter deci centi milli

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Example for Length So 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

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Example for Length But what if you need to measure a longer distance, like from your house to a mall? Let’s say you live approximately 10 miles from the mall 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: 16093 meters = kilometers (or 16.1 if rounded to 1 decimal place)

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Powers of 10 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

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For Example A centimeters is 10 times longer than a millimeter so it takes more millimeters for the same length 1 centimeter = 10 millimeters Example not to scale 1 mm 1 cm 40 41

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**The “Steps” 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 ( 1 x 10 = 10) = (10 x 10 = 100) (2 x 10 = 20) = (20 x 10 = 200) kilo hecto deca meter liter gram deci centi milli

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More “Steps” 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 hecto deca meter liter gram deci centi milli

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Applying “Steps” Now let’s try our previous example from meters to kilometers: 16093 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 hecto deca meter liter gram deci centi milli

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Moving to the “Steps” 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

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Moving the “Steps” Now let’s start from centiliters and convert to kiloliters centiliters = kiloliters centiliters = 4 kiloliters kilo hecto deca meter liter gram deci centi milli

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Moving the “Steps” Now let’s start from meters and convert to kilometers 4000 meters = 4 kilometers kilo hecto deca meter liter gram deci centi milli Now let’s start from centigrams and convert to grams 4000 centigrams = 40 grams kilo hecto deca meter liter gram deci centi milli

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**Keep on Moving the “Steps”**

Now let’s start from liters and convert to centiliters 5 liters = 500 centiliters kilo hecto deca meter liter gram deci centi milli Now let’s start from kilograms and convert to grams kilograms = 300 grams kilo hecto deca meter liter gram deci centi milli

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Keep on Moving Now let’s start from kilometers and convert to millimeters 4 kilometers = millimeters or 4 kilometers = 40 hectometers = 400 decameters = 4000 meters = 40000 decimeters = centimeters = millimeters kilo hecto deca meter liter gram deci centi milli

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**Finally Summary Base units in the metric system are meter, liter, gram**

Metric system is based on powers of 10 For conversions within the metric system, each “step” is 1 decimal place to the right or left Using the diagram below, converting to the right, moves the decimal to the right and vice versa kilo hecto deca meter liter gram deci centi milli

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The Metric System.

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