1. The METRIC SYSTEM & CONVERSIONS
MSJC ~ San Jacinto Campus
Math Center Workshop Series
Janice Levasseur

2. The Metric System
The metric system is an internationally standardized system of units of measurement.
The metric system is based on a base unit and prefixes.

3. Prefixes Kilo - 1000 k Hecto - 100 h Deca - 10 da 1 Deci - 0.1 d
Centi c
Milli m

4. Length The basic unit of length in the metric system is the meter (m)
Metric Units of Length
Kilometer (km) = 1000 m
Hectometer (hm) = 100 m
Decameter (dam) = 10 m
Meter (m) = 1 m
Decimeter (dm) = 0.1 m
Centimeter (cm) = 0.01 m
Millimeter (mm) = m

5. Mass
Weight is a measure of how strongly gravity is pulling on an object (decreases as elevation increases)
Mass is the amount of material in an object (doesn’t change)
Note: on Earth, weight and mass are used interchangeably

6. Mass The basic unit of mass in the metric system is a gram (g)
1 g = mass of water in a cube that measures 1 cm x 1 cm x 1cm
Metric Units of Mass
Kilogram (kg) = 1000 g
Hectogram (hg) = 100 g
Decagram (dag) = 10 g
Gram (g) = 1 g
Decigram (dg) = 0.1 g
Centigram (cg) = 0.01 g
Milligram (mg) = g

7. Capacity Liquid substances are measured in units of capacity.
The basic unit of mass in the metric system is a liter (L)
1 L = capacity of a cube that measures 10 cm x 10 cm x 10 cm
Metric Units of Capacity
Kiloliter (kL) = 1000 L
Hectoliter (hL) = 100 L
Decaliter (daL) = 10 L
Liter (L) = 1 L
Deciliter (dL) = 0.1 L
Centiliter (cL) = 0.01 L
Milliliter (mL) = L

8. Conversions within the Metric System
To convert units within the metric system, write the prefixes in order from largest to smallest
k h da d c m
To convert from a smaller unit to a larger unit, move to the left
To convert from a larger unit to a smaller unit, move to the right

9. Ex: Convert 1600 cm to m km hm dam m dm cm mm
Move 2 places to the left to get from cm to m
Therefore, move the decimal point in 1600 two places to the left to convert from cm to m
1600 cm = m

10. Ex: Convert 2 kL to L kL hL daL L dL cL mL
Move 3 places to the right to get from kL to L
Therefore, move the decimal point in 2 three places to the right to convert from kL to L
2 KL = 2000 L

11. Ex: Convert 241 g to mg kg hg dag g dg cg mg
Move 3 places to the right to get from g to mg
Therefore, move the decimal point in 241 three places to the right to convert from g to mg
241 g = 241,000 mg

12. Ex: Convert 3 mL to L kL hL daL L dL cL mL
Move 3 places to the left to get from mL to L
Therefore, move the decimal point in 3 three places to the left to convert from mL to L
3 mL = L

13. Ex: Convert 45 cm to km km hm dam m dm cm mm
Move 5 places to the left to get from cm to km
Therefore, move the decimal point in 45 five places to the left to convert from cm to km
45 cm = km

14. Ex: Convert 5.4 kg to dg kg hg dag g dg cg mg
Move 4 places to the right to get from kg to dg
Therefore, move the decimal point in 5.4 four places to the right to convert from kg to dg
5.4 kg = dg

15. Conversions between the U.S. Customary System and the Metric System
Approximate equivalences between the U.S. Customary System and the Metric System are needed for conversion between systems
Dimensional Analysis will be used to compute the conversion

16. Equivalences Units of Weight Units of Capacity Units of Length
1 oz g
1 lb g
2.2 lb kg
Units of Capacity
1.06 qt L
1 gal L
Units of Length
1 in = 2.54 cm
3.28 ft m
1.09 yd m
1 mi km

17. Dimensional Analysis
Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value (Multiplication Property of 1 – the Magic One.)
Use the units to dictate the form of the Magic One

18. Ex: Convert 130 lbs to kg (round to the nearest whole number)
Write the original measurement as a unit fraction
Multiply the unit fraction by a magic one – the form of which is dictated by the units
the numerator unit is the unit you want
the denominator unit is the unit you want to eliminate
Write your answer in the specified form (decimal number)

19. Ex: Convert 130 lbs to kg (round to the nearest whole number)

20. Ex: Convert 60 km to mi (round to the nearest whole number)
Write the original measurement as a unit fraction
Multiply the unit fraction by a magic one – the form of which is dictated by the units
the numerator unit is the unit you want
the denominator unit is the unit you want to eliminate
Write your answer in the specified form (decimal number)

21. Ex: Convert 60 km to mi (round to the nearest whole number)

22. Ex: Convert 5.4 kg to lb (round to the nearest tenth place)
Write the original measurement as a unit fraction
Multiply the unit fraction by a magic one – the form of which is dictated by the units
the numerator unit is the unit you want
the denominator unit is the unit you want to eliminate
Write your answer in the specified form (decimal number)

23. Ex: Convert 5.4 kg to lb (round to the nearest tenth place)

24. Ex: Convert 45 cm to in (round to the nearest tenth place)
Write the original measurement as a unit fraction
Multiply the unit fraction by a magic one – the form of which is dictated by the units
the numerator unit is the unit you want
the denominator unit is the unit you want to eliminate
Write your answer in the specified form (decimal number)

25. Ex: Convert 45 cm to in (round to the nearest tenth place)

26. Ex: As a practical joke, on the show Candid Camera, a gas station listed their price as $1.79/Liter. People gassing up thought they were getting a great deal, but then were outraged when their total owed came up. WHY?
What do you notice about the listed price?
What should we do?

27. Listed their price as $1.79/Liter.

28. Ex: The price of a certain medication is $35 per Liter
Ex: The price of a certain medication is $35 per Liter. Find the price per fluid ounce.
But now what? There isn’t a direct equivalence from Liters to fluid ounces.
We can use several equivalences stepping down to fluid ounces
Liters  Quarts  Pints  Cups  fluid ounces