PRESENTATION 8 Metric Measurement Units METRIC UNITS OF

PRESENTATION 8 Metric Measurement Units

METRIC UNITS OF LINEAR MEASURE • Based on powers of 10 • Most frequently used units of length: • • kilometer 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 twodimensional 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 (dm 2) as square meters (m 2) • • Since a square meter is the next largest unit to a square decimeter, move the decimal point 2 places to the left 840. 5 dm 2 = 8. 405 m 2 In moving the decimal point 2 places to the left, you are actually dividing by 100

METRIC AREA CONVERSIONS • Example: Express 46 square centimeters (cm 2) as square millimeters (mm 2) • • Since a square millimeter is the next smallest unit to a square centimeter, move the decimal point 2 places to the right 46 cm 2 = 4, 600 mm 2 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 threedimensional

METRIC VOLUME UNITS • Example: Express 27, 000 cubic centimeters (cm 3) as cubic meters (m 3) • • 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 cm 3 = 0. 027 m 3 In moving the decimal point 6 places to the left, you are actually dividing by 1, 000 or 1, 000

• METRIC UNITS Commonly used capacity-cubic measure equivalents: 1 milliliter (m. L) = 1 cubic centimeter (cm 3) 1 liter (L) = 1 cubic decimeter (dm 3) 1 liter (L) = 1, 000 cubic centimeters (cm 3) • 1, 000 liters (L) = 1 cubic meter (m 3) 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 (in 3) = 16. 387 cm 3 1 fl oz = 29. 574 cm 3 1 tsp = 4. 929 m. L 1 tbsp = 14. 787 m. L 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 ft 2 to square centimeters • This requires two unity fractions

PRACTICAL PROBLEMS • • • An assembly consists of 5 metal plates The respective plates are 650 cm 2, 800 cm 2, 16. 3 dm 2, 12 dm 2, and 0. 12 m 2 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 m 2 + 0. 080 m 2 + 0. 163 m 2 + 0. 12 m 2 = 0. 548 m 2 ≈ 0. 55 m 2 The sum of the measures of the 5 plates is about 0. 55 m 2