PRESENTATION 8 Metric Measurement Units

METRIC UNITS OF LINEAR MEASURE Based on powers of 10 Most frequently used units of length: kilometer meter centimeter millimeter

METRIC LINEAR UNITS The following list shows several units of linear measure and their lengths in meters: 1 kilometer (km) = 1,000 meters (m) 1 hectometer (hm) = 100 meters (m) 1 dekameter (dam) = 10 meters (m) 1 meter (m) = 1 meter (m) 1 decimeter (dm) = 0.1 meter (m) 1 centimeter (cm) = 0.01 meter (m) 1 millimeter (mm) = 0.001 meter (m)

CONVERTING METRIC LENGTHS Since the metric system is based on powers of 10, the easiest method of converting between metric units is by moving the decimal point To express a given unit as a larger unit, move the decimal point to left the number of places between the two units To express a given unit as a smaller unit, move the decimal point to right the number of places between the two units

CONVERTING METRIC LENGTHS Example: Express 65 decimeters as meters Move the decimal 1 place to the left since a meter is the next larger unit to a decimeter 65 dm = 6.5 m Example: Express 0.28 decimeters as centimeters Move the decimal 1 place to the right since a centimeter is the next smaller unit to a decimeter 0.28 dm = 2.8 cm

METRIC SURFACE AREA As with linear measure, the easiest method of converting between metric units of surface area is by moving the decimal point To express a given unit as the next larger unit, move the decimal point two places to the left. Move two places because surface area is two- dimensional To express a given unit as the next smaller unit, move the decimal point two places to the right

METRIC AREA CONVERSIONS The table below reviews some common metric units, listing them from larger to smaller in order from left to right

METRIC AREA CONVERSIONS Example: Express 840.5 square decimeters (dm2) as square meters (m2) Since a square meter is the next largest unit to a square decimeter, move the decimal point 2 places to the left 840.5 dm2 = 8.405 m2 In moving the decimal point 2 places to the left, you are actually dividing by 100

METRIC AREA CONVERSIONS Example: Express 46 square centimeters (cm2) as square millimeters (mm2) Since a square millimeter is the next smallest unit to a square centimeter, move the decimal point 2 places to the right 46 cm2 = 4,600 mm2 In moving the decimal point 2 places to the right, you are actually multiplying by 100

METRIC VOLUME UNITS As with linear and area measure, the easiest method of converting between metric units of volume is by moving the decimal point For volume, the decimal will be moved three places because volume is three- dimensional

METRIC VOLUME UNITS Example: Express 27,000 cubic centimeters (cm3) as cubic meters (m3) Since a cubic meter is 2 units larger than a cubic centimeter, the decimal point is moved 2 x 3 or 6 places to the left 27,000 cm3 = 0.027 m3 In moving the decimal point 6 places to the left, you are actually dividing by 1,000  1,000 or 1,000,000

METRIC UNITS Commonly used capacity-cubic measure equivalents: 1 milliliter (mL) = 1 cubic centimeter (cm3) 1 liter (L) = 1 cubic decimeter (dm3) 1 liter (L) = 1,000 cubic centimeters (cm3) 1,000 liters (L) = 1 cubic meter (m3) Commonly used weight (mass) measure equivalents: 1,000 milligrams (mg) = 1 gram (g) 1,000 grams (g) = 1 kilogram (kg) 1,000 kilograms (kg) = 1 metric ton (t)

COMPOUND UNITS Products or quotients of two different units Converted to smaller or larger equivalent compound unit measures, use the unity fractions Expressed using per, such as kilometers per hour, which indicates division Kilometers per hour can be written:

COMPOUND UNIT EQUIVALENTS Simple compound needs only one unit to be converted Complex compound needs more than one unit to be converted

COMPOUND UNIT EQUIVALENTS Example: Express 62.35 kilometers per hour as meters per minute Multiply 62.35 km/hr by the unity fractions = 1,039.1 ≈ 1,039 m/min

METRIC-CUSTOMARY CONVERSIONS Length 1 in = 2.54 cm 1 ft = 30.48 cm 1 yd = 0.9144 m 1 mi = 1.6093 km Weight 1 oz = 28.35 g 1 lb = 0.4536 kg 1 (short) ton = 907.2 kg Volume 1 cu in (in3) = 16.387 cm3 1 fl oz = 29.574 cm3 1 tsp = 4.929 mL 1 tbsp = 14.787 mL 1 qt = 0.9464 L 1 gal = 3.785 L

METRIC-CUSTOMARY CONVERSIONS Example: Convert 7.36 in to millimeters This requires two unity fractions

METRIC-CUSTOMARY CONVERSIONS Example: Convert 12.75 ft2 to square centimeters This requires two unity fractions

PRACTICAL PROBLEMS An assembly consists of 5 metal plates The respective plates are 650 cm2, 800 cm2, 16.3 dm2, 12 dm2, and 0.12 m2 Determine the total surface measure, in square meters, of the 5 plates

PRACTICAL PROBLEMS Convert each measure to square meters

PRACTICAL PROBLEMS Sum the measures 0.0650 m2 + 0.080 m2 + 0.163 m2 + 0.12 m2 + 0.12 m2 = 0.548 m2 ≈ 0.55 m2 The sum of the measures of the 5 plates is about 0.55 m2