Unit 9 METRIC MEASUREMENT UNITS 1 METRIC UNITS

Unit 9 METRIC MEASUREMENT UNITS 1

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

METRIC LINEAR UNITS • n The following list shows several units of linear measure and their lengths in meters: 1 kilometer (km) = 1000 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) There a lot of these conversions on your conversion sheet with the back covering the prefixes and some of the conversions covered on the front. In metric, the unit is not as important as the prefix. 3

CONVERTING METRIC LENGTHS • Express 1. 95 centimeters as millimeters Express 75 decimeters as meters **Notice I converted to meters and back to millimeters. This is not required, you can slide the • decimals but most non-metric using people have trouble sliding the decimal. Especially when we get to other dimensions. The conversions used above are on your conversion sheet and keep you from sliding the wrong direction. 4

METRIC AREA CONVERSIONS • Express 84. 5 square centimeters as square decimeters • Express 5. 6 square hectometers as square Dekameters • Capital D to show Deka instead of deci • These conversions are not all on your sheet but to go from first to second • Dam is also used for Dekameters dimension you are squaring measurements from the first…. so 10 dm in a meter in linear (first) so 100 dm 2 = 1 m 2 5

METRIC VOLUME UNITS n Express 38, 500 cubic millimeters as cubic decimeters n Convert 2. 5 km 3 as cm 3 (also called cc) 6

METRIC UNITS • Commonly used capacity-cubic measure equivalents: q q • 1 milliliter (m. L) 1 liter (L) 1000 liters (L) = 1 cubic centimeter (cm 3) = 1 cubic decimeter (cm 3) = 1000 cubic centimeters (cm 3) = 1 cubic meter (m 3) Commonly used weight (mass) measure equivalents: q q q 1000 milligrams (mg) 1000 grams (g) 1000 kilograms (kg) = 1 gram (g) = 1 kilogram (kg) = 1 metric ton (t) 7

COMPOUND UNITS • Products or quotients of two different units – – Converted to smaller or larger equivalent compound unit measures using unity fractions Expressed using per such as kilometers per hour which indicates division • Kilometers per hour can be written: 8

Simple needs only one unit to be converted • Complex needs more than one unit to be converted COMPOUND UNIT EQUIVALENTS • Express 78. 36 kilometers per hour as meters per minute 9

Extremely large and small measures n Top and bottom of chart on conversion sheet q Tera, Giga, Mega are very large (heard in computer world and astrology) q micro, nano, pico are very small (heard in biology) They work the same in unity fraction method just more conversions. With these you will use scientific notation in most cases. It is 2. 4 x 1020 m to the sun. How far is that in Terameters? n A cell is 5. 7 micrometers thick. How many picometers is that? n n 10

METRIC-CUSTOMARY CONVERSIONS n n Length q 1 in = 2. 54 cm q 1 ft = 30. 48 cm q 1 yd = 0. 9144 m q 1 mi = 1. 6093 km Weight q 1 oz = 28. 35 g q 1 lb = 0. 4536 kg q 1 (short) ton = 907. 2 kg n Volume q 1 cu in. (in 3) = 16. 387 cm 3 q 1 fl oz = 29. 574 cm 3 q 1 tsp = 4. 929 m. L q 1 tbsp = 14. 787 m. L q 1 qt = 0. 9464 L q 1 gal = 3. 785 L 11

EXAMPLES n n Convert 8. 24 in to millimeters Convert 9. 25 ft 2 to square centimeters 12

PRACTICE PROBLEMS 1. 2. 3. 4. 5. 6. 7. Express 63 meters as centimeters Express 4. 75 Dekameters as kilometers Express 0. 0076 hectometers as millimeters Express 49. 3 decimeters as Dekameters Express 0. 084 square decimeters as square centimeters Express 1. 09 square Dekameters as square hectometers Express 2. 5 cubic feet as cubic meters 13

PRACTICE PROBLEMS (Cont) 8. 9. 10. 11. 12. 13. 14. Express 123, 500 cubic inches as cubic centimeters Express 1, 260 cm 3 as dm 3 Express 1. 268 cubic meters as cubic centimeters Express 13. 5 liters as gallons Express 4. 6 cubic meters as cubic inches Express 18. 2 ft/min as km/hr Express 1. 2 short tons/cubic foot as pounds/cubic inch 14

PRACTICE PROBLEMS (Cont) 15. 16. 17. 18. 19. 20. A bullet travels at 1500 miles per hour. How many meters per second is that? You receive measurements that specify a 2. 5 square meter area for a new machine. How many square inches do you need to clear out? A map in Canada says it is 350 kilometers to the next city. How many miles is the trip? A cell has a thickness of 3. 2 nanometers. In scientific notation, how many meters is that? If a circuit needs 0. 5 Megawatts, how many deciwatts are needed? If I have a tank that holds 350 gallons, how many milliliters does it hold? 15

PROBLEM ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 6300 cm 0. 0475 km 760 mm 0. 493 dam 8. 4 cm 2 0. 0109 hm 2 0. 07079 m 3 2. 024 m 3 1. 26 dm 3 1268000 cm 3 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 3. 57 gal 280710 cu in 19. 97 km/hr 1. 389 lb/ cu in 670. 57 m/sec 3875. 04 in 2 217. 49 mi 3. 2 x 10 -9 m 5. 0 x 106 dw 1324750 m. L 16