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PRESENTATION 8 Metric Measurement Units

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:

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PRESENTATION 8 Metric Measurement Units

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  1. PRESENTATION 8Metric Measurement Units

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

  3. 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)

  4. 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

  5. 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

  6. 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

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

  8. 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

  9. 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

  10. 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 threeplaces because volume is three-dimensional

  11. 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

  12. 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)

  13. 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 perhour, which indicates division • Kilometers per hour can be written:

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

  15. 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

  16. METRIC-CUSTOMARY CONVERSIONS • 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 • 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

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

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

  19. 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

  20. PRACTICAL PROBLEMS • Convert each measure to square meters

  21. 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

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