Multiply each of the following numbers by 10

27 x 10 =

157 x 10 =

56.4 x 10 =

458.87 x 10 =

23.516 x 10 =

270

1570

564

4588.7

235.16

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

330 10 =7600 10 =268.1 10 =1.78 10 =

18.395 10 =

33.0 or 33760.0 or 76026.810.1781.8395

210 100 =7800 100 =521.6 100 =

82.1 100 =7.666 100 =

2.10 or 2.1

78.00 or 78

4.216

0.821

0.07666

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

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

The three prefixes that we will use the most in class are:kilocentimilli

kilo hecto deca

Base Units

metergramliter

deci centi milli

So if you needed to measure length you would choose meter as your base unitLength 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 a mall?Let’s say you live approximately 10

miles from the mall 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)

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 Unitsmetergramliter

deci centi milli

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 mm1 mm1 mm1 mm1 mm1 mm1 mm1 mm1 mm1 mm

1 cm

40

41

41

40

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 decameterliter

gramdeci centi milli

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

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

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 decameterliter

gramdeci centi milli

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

meterliter

gram

deci centi milli

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

meterliter

gram

deci centi milli

Now let’s start from centiliters and convert to kiloliters

400000 centiliters = 4.00000 kiloliters

400000 centiliters = 4 kiloliters

kilo hecto deca

meterliter

gram

deci centi milli

Now let’s start from meters and convert to kilometers

4000 meters = 4 kilometers

kilo hecto deca

meterliter

gram

deci centi milli

kilo hecto deca

meterliter

gram

deci centi milli

• Now let’s start from centigrams and convert to grams

4000 centigrams = 40 grams

Now let’s start from liters and convert to centiliters

5 liters = 500 centiliters

kilo hecto deca

meterliter

gram

deci centi milli

kilo hecto deca

meterliter

gram

deci centi milli

• Now let’s start from kilograms and convert to grams

.3 kilograms = 300 grams

Now let’s start from kilometers and convert to millimeters4 kilometers = 4000000 millimeters

or4 kilometers = 40 hectometers = 400 decameters = 4000 meters = 40000 decimeters = 400000 centimeters = 4000000 millimeters

kilo hecto deca

meterliter

gram

deci centi milli

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

meterliter

gram

deci centi milli

http://www.powersof10.com/