Metrics
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The metric system uses a set of base units and prefixes to denote multiples or fractions of the base units. The base units are the meter for length, liter for volume, and gram for mass. Prefixes denote powers of 10, so moving one "step" to the left or right in the prefix diagram corresponds to moving the decimal place one position in conversions between units. For example, 1 meter = 10 decimeters = 100 centimeters. The document provides examples of converting within the metric system using this concept of moving the decimal place for each prefix "step."
Metrics
- 2. Metric System The metric system is based on a base unit that corresponds to a certain kind of measurement Length = meter Volume = liter Weight (Mass) = gram Prefixes plus base units make up the metric system Example: Centi + meter = Centimeter Kilo + liter = Kiloliter
- 3. Metric System The three prefixes that we will use the most are: kilo centi milli kilo hecto deca Base Units meter gram liter deci centi milli
- 4. Metric System 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
- 5. Metric System But what if you need to measure a longer distance, like from your house to school? Lets 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)
- 6. 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
- 7. 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 cm 40 41 41 40 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm
- 8. Metric System For each step to right, you are multiplying by 10 For example, lets 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
- 9. 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 hecto deca meter liter gram deci centi milli
- 10. Metric System Now lets 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
- 11. 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
- 12. Metric System Now lets start from centimeters and convert to kilometers 400000 centimeters = 4 kilometers 400000 centimeters = 4.00000 kilometers kilo hecto deca meter liter gram deci centi milli
- 13. Metric System Now lets start from meters and convert to kilometers 4000 meters = 4 kilometers Now lets start from centimeters and convert to meters 4000 centimeters = 40 meters kilo hecto deca meter liter gram deci centi milli kilo hecto deca meter liter gram deci centi milli
- 14. Metric System Now lets start from meters and convert to centimeters 5 meters = 500 centimeters Now lets start from kilometers and convert to meters .3 kilometers = 300 meters kilo hecto deca meter liter gram deci centi milli kilo hecto deca meter liter gram deci centi milli
- 15. Metric System Now lets start from kilometers and convert to millimeters 4 kilometers = 4000000 millimeters or 4 kilometers = 40 hectometers = 400 decameters = 4000 meters = 40000 decimeters = 400000 centimeters = 4000000 millimeters kilo hecto deca meter liter gram deci centi milli
- 16. Metric System 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