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