The METRIC SYSTEM & CONVERSIONS

MSJC ~ San Jacinto CampusMath Center Workshop Series

Janice Levasseur

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.

Prefixes

• Kilo - 1000 k

• Hecto - 100 h

• Deca - 10 da

• 1

• Deci - 0.1 d

• Centi - 0.01 c

• Milli - 0.001 m

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) = 0.001 m

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

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) = 0.001 g

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) = 0.001 L

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

Ex: Convert 1600 cm to m

• km hm dam m dm cm mm

1600 cm = 16.00 m

• 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

Ex: Convert 2 kL to L

• kL hL daL L dL cL mL

2 KL = 2000 L

• 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

Ex: Convert 241 g to mg

• kg hg dag g dg cg mg

241 g = 241,000 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

Ex: Convert 3 mL to L

• kL hL daL L dL cL mL

3 mL = 0.003 L

• 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

Ex: Convert 45 cm to km

• km hm dam m dm cm mm

45 cm = 0.00045 km

• 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

Ex: Convert 5.4 kg to dg

• kg hg dag g dg cg mg

5.4 kg = 54000 dg

• 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

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

Equivalences

• Units of Weight– 1 oz 28.35 g– 1 lb 454 g– 2.2 lb 1 kg

• Units of Capacity– 1.06 qt 1 L– 1 gal 3.79 L

• Units of Length– 1 in = 2.54 cm– 3.28 ft 1 m– 1.09 yd 1 m– 1 mi 1.61 km

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

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)

22130

221

1130

.kg

lbs.kglbs

= 59.0 kg

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

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)

61160

6111

160

.mi

km.mikm

= 37.2 mi

= 37 mi

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

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)

18811

122

145 lb.

kglb.kg.

= 11.88 lb

= 11.9 lb

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

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)

54245

5421

145

.in

cm.incm

= 17.71 in

= 17.7 in

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

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 should we do?

• What do you notice about the listed price?

Listed their price as $1.79/Liter.

galL.

L.$

1793

1791

gal.$

1786

Ex: The price of a certain medication is $35 per Liter.

Find the price per fluid ounce.

L$135

qt.L0611

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

ptqt21

Cpt21

ozflC

81

ozfl.$923335

ozfl/.$ 031