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Unit 1 – Lesson 2 Relating Metric and Imperial Systems

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Unit 1 – Lesson 2 Relating Metric and Imperial Systems Unit 1 – Lesson 2 Relating Metric and Imperial Systems Most of the scientific community of the world uses the metric system for measurement. Developed by the French in the 18th century, the Système International d’unités, (SI units), is known for its prefixes based on powers of ten and convenient calculation. Developed in the 18th century, the Metric System was introduced to Canada around 1970. Despite that fact, most of you still know your weight in pounds, not in kilograms a testimony to the need to be familiar with both systems. A. System Units System Links Imperial System Metric System Prefix Symbol Magnitude 1 inch = 2.54 cm Length yotta Y 1024 1 mile = 1.6021 km 1 foot = 12 inches zetta Z 1021 1 kg = 2.2046 lbs 1 yard = 3 feet exa E 1018 1 gal = 4.545 L 1 fathom = 2 yards 15 peta P 10 1 rod = 5.5 yards tera T 1012 1 chain = 22 yards giga G 109 1 furlong = 220 yards mega M 106 1 furlong = 40 rods 3 kilo k 10 1 mile = 5280 feet 2 hecto h 10 1 Volume deca da 10 0 1 gallon = 4 quarts - - 10 deci d 10-1 1 quart = 2 pints centi c 10-2 1 pint = 2 cups milli m 10-3 1 pint = 20 fluid ounces micro μ 10-6 -9 nano n 10 Mass μμ -12 pico p 10 1 pound = 16 ounces femto f 10-15 1 ton = 2000 pounds atto a 10-18 zepto z 10-21 yocto y 10-24 Note: 1 mL = 1cm3 B. Estimation To estimate is to make a reasonable guess that is close to the actual value without an exact calculation. Usually we use a referent to aid us in our estimation. As with most things practice makes perfect. The more you estimate, the more you improve your accuracy, that is, the closer you get to the actual value. The following is an exercise designed to help you to develop your estimation skills. Estimate the following in both Metric and Imperial units: Item Estimated Length Actual Length Room Height m ft m ft Room Width m ft m ft Book Height cm in cm in Whiteboard m ft m ft Winnipeg to km mi km mi Chicago Item Estimated Weight Actual Weight Pencil g oz g oz Textbook kg lbs kg lbs Mr. Warkentine kg lbs kg lbs Titanic T t T t C. Metric Rulers Write the measurement in centimeters indicated by the arrows. A _____ B _____ C ______ D ______ E _____ F ______ G ______ D. Unit Conversion – Dimensional Analysis Dimensional analysis is extremely useful for the conversion of units in the same or different measurement system. It is also useful as a guide to solving word problems if proper cancellation of units is followed. To use a simple example, let’s convert 3.2 km into meters. Method: 1. Write the given number and unit twice separated by an equals sign. (3.2 km = 3.2 km) 2. Multiply this by a conversion factor – a fraction used to convert one unit to another. This conversion factor is equal to one so technically we are not altering the number – only the units. a. Set up the division sign of a blank fraction, (conversion factor). b. Place the given unit (km) as denominator of the conversion factor c. Place desired unit as numerator (m). d. Place a 1 in front of the larger unit, (Use table on formula sheet) e. Determine the number of smaller units needed to make ‘1’ of the larger units, often a power of 10. f. Determine the dimension and place it as an exponent to (e). In this case the unit is length with a dimension of 1 so it is left off and understood to be there already. Dimension Exponent length, time, 1 mass, etc area 2 volume 3 3. Multiply all numerators and denominators canceling units to solve problem. * Some problems require more than one conversion factor. ie: 12 m/s into km/hr *A problem involving volume. ie: 150 ft3 to yd3 *A word problem. A plane travels at 320 km/h. How many seconds would it take to travel two kilometers? ie: Assignment: 1. 25 cm into mm 14. 5.2 x 108 Hz into GHz 2. 46 min to s 15. 4.77 x 1015 pL into L 3. 365 days to s 16. 3.69 Tm into hm 4. 76 years to min 17. 4264 Mm into feet 5. 6.0 ft to cm 18. 6.5 x 1018 nL to cm3 6. 77 furlongs to fm 19. 2.50 x 107 km3 into m3 7. 4500 g into kg 20. 4600 cm2 into pm2 8. 15 dag into hg 21. 29 yard2 into dm2 9. 2000000 bytes into Mb 22. 7 nm3 into dam3 10. 3000000000 Hz into GHz 23. 3.2 Gm3 into hm3 11. 40 miles per hour into km/hr 24. 2.5 x 1024 ft3 into Mm3 12. 90 km/h into m/s 13. 1120 cm into km Part B: Word Problems – Solve using dimensional analysis. 1. The density of an object is 3.25 grams per cm3. If the mass of the object is 65 grams, what is the volume? 2. A car averages 35 miles per gallon (Imp.) a) How far would you be able to travel with 16 gallons? b) How far could you travel on 55.5 L? c) What is 35 miles/gal in liters per 100 km? 3. The speed of sound is 343 m/s at sea level at 20º C. Convert to km/h. 4. A car’s average speed is 45 km/hr. How far could it go in 2.5 hours? Answers: Part A: 1) 250 mm 2) 2760 s 3) 3.15 x 107 s 4) 4.0 x 107 min 5) 183 cm 6) 1.55 19 -2 x10 fm 7) 4.5 kg 8) 1.5 hg 9) 2 Mb 10) 3 GHz 11) 64 km/h 12) 25 m/s 13) 1.12x10 km 14) 0.52 GHz 15) 4.77x103 L 16) 3.69x1010 hm 17) 1.4x1010 cm 18) 6.5x1012 cm3 19) 2.5x1016 m3 20) 4.6x1023 pm2 21) 2.4x107 dm2 22) 7x10-30 dam3 23) 3.2x1021 hm3 24) 7.1x104 Mm3 Part B: 1) 20 cm3 2a) 560 mi b) 427 mi c) 8.1L/100 km 3) 1240 km/h 4) 110 km .
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