1.1 Imperial Measurements

Transcription

1 1.1 Imperial Measurements Unit Abbreviation Referent inch in. foot ft yard yd. or yds. mile mi. length of thumb knuckle to end of thumb length of foot tip of nose to end of finger when outstretched 20 minutes of walking A common abbreviation for 5 ft. 2 in. Is 5 2 NOTE: 5 ft. 2 in. is not the same as 5.2 ft. see figure 1. Conversions 12 in. = 1 ft. 3 ft. = 1 yd ft. = 1 mi. These are exact conversions. A. Conversions by Unit analysis Eg. Convert 5 yards to feet. 5 yds. 3 ft. 15 ft. 1 yd. Eg. Convert 5 yards to inches. 5 yds. 3 ft. 12 in. 180 in. 1 yd. 1 ft. Eg. Convert 51 inches to feet. (round to the nearest foot) 51 in. 1 ft. 12 in ft. which rounds to 4 feet. Eg. Convert 51 inches to feet and inch measurement. 51 in. 1 ft. 12 in ft. 12 in. 1 ft ft. which is 4 feet and 0.25 feet. 3 in. which changes the part of a foot to inches. Thus 3 inches. Therefore 51 inches is 4 feet 3 inches in length.

2 Eg. Convert 51 inches to yards, feet, and inches. 51 in. 1 ft. 1 yd yds. 12 in. 3 ft. which is 1 yard and yards yds. 3 ft ft. 1 yd. which is 0 feet and feet ft. 12 in. 10 in. 1 ft. which is 10 inches. Therefore 51 inches is 1 yard 0 feet 10 inches. Eg. The perimeter of the framed picture will be 136 in. a) What will be the perimeter of the framed picture in feet and inches? 136 in. 1 ft ft. 12 in. which is 11 feet and feet ft. 12 in. 4 in. 1 ft. which is 4 inches Therefore 136 inches is 11 feet 4 inches. b) The framing material is sold by the foot. It costs $1.89/ft. What will be the cost of material before taxes? Since the materials are sold per foot, we need 12 ft. 12 ft. $1.89 $ ft. Notice $1.89/ft. can be $1.89 written as 1 ft. Thus the total cost will be $ Eg. 6 yds. of fabric need to be cut into 5 inch strips. How many strips are possible? 6 yds. 3 ft. 12 in. 216 in. 1 yd. 1 ft. since , there will be 43 strips created.

3 B. Conversions by proportions Best to use when only one step between units is needed. Eg. Convert 5 yds to ft. 3 ft. x 1 yd. 5 yds. x 35 x 15 ft. Eg. Convert 15 ft. to in. 12 in. x 1 ft. 15 ft. x x 180 in. Eg. Change 51 in. to yds. ft. in. 12 in. 51 in. 1 ft. x 12x x 4.25 ft. 12 Since 3 feet is a yard, then 4.25 ft. breaks down to 1 yd. 1 ft. 0.25ft. Converting the remaining 0.25 ft. to inches 12in. x 1 ft ft. x x 3 in. Finally this gives 1 yd. 1 ft. 3 in.

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6 created by Acces for use by Edwin Parr Comp School only.

7 ID: A Metric Conversions Review Math 10C Name: 1. Convert kilometres to centimetres 8. Convert 5500 millimetres to centimetres 2. Convert 0.71 metres to millimetres 9. Convert 3.5 metres to millimetres 3. Convert 9500 centimetres to metres 10. Convert centimetres to millimetres 4. Convert millimetres to metres 11. Convert 0.2 millimetres to centimetres 5. Convert millimetres to centimetres 12. Convert centimetres to kilometres 6. Convert 370 metres to centimetres 13. Convert 60 centimetres to metres 7. Convert metres to centimetres 14. Convert 880 metres to kilometres 15. Convert millimetres to metres 1

8 ID: A Metric Conversions Review Answer Section cm mm m m cm 6. 37,000 cm cm cm 9. 3,500 mm mm cm km m km m 1

9 ID: A Referents Math 10C Name: 1. The length of a large person's shoe is close to the measure of A. 1 in. B. 1 ft. C. 1 yd. D. 1 mi. 2. After walking for 20 minutes a person will have travelled approximately A. 500 ft. B. 500 yds. C. 1 yd. D. 1 mi. 3. The length from the tip of a nose to an outstretched finger tip is a referent for A. 1 in. B. 1 ft. C. 1 yd. D. 1 mi. 4. The length of a thumb from the tip to the first joint is a referent for A. 1 in. B. 1 ft. C. 1 yd. D. 1 mi. 5. Ordering prints for photographs have the typical sizes of 4 6, 5 7, or The units for these are in A. inches. B. feet. C. yards. D. miles. 6. A common board used in construction is a 2 4 (pronounced two-by-four). The actual dimensions of the wood are The units for these 2 2 meaurements are in A. inches. B. feet. C. yards. D. miles. 7. A typical sheet of plywood lumber sold is 4 8 (pronounced four-by-eight). The units for this are in A. inches. B. feet. C. yards. D. miles. 8. The typical length of a garden hose is A. 50 in. B. 50 ft. C. 100 in. D. 100 yds. 9. In North America there are standard sizes of paper. Which of the following is not a standard size of paper? A inches 2 B. 8 9 inches C inches 2 D inches 10. When purchasing wood at a lumber store, the length of a board is considered. A typical length of a board sold is A. 12 ft. B. 12 yds. C. 50 yds. D. 50 ft. 11. When buying a house on a town or city block, frontage is an important consideration. Frontage is the length of the plot of land measured along the roadside at the front of the plot. A typical frontage for a small house on a city block is A. 50 ft. B. 50 in. C. 500 ft. D. 500 yds. 1

10 ID: A 12. The length of a typical North American football playing field from goal line to goal line is A. 10 ft. B. 10 in. C. 100 ft. D. 100 yds. 13. Computer LCD monitors are typically sold by their diagonal length. A common size of monitors sold today is A. 20 ft. B. 20 in. C. 200 ft. D. 200 in. 14. A common size of a bedroom in a typical house is A. 19 ft. 40 ft. B. 10 ft. 12 ft. C. 19 yds. 40 yds. D. 10 yds. 12 yds. 15. A common height of a room in a typical house is A. 4 ft. B. 6 ft. C. 8 ft. D. 13 ft. 16. A common width of a doorway in typical house is A. 30 in. B. 4 ft. C. 30 ft. D. 4 yds. 17. A double garage door has a standard width. This entrance that allows cars to enter the garage has a width of A. 4 ft. B. 16 ft. C. 16 yds. D. 4 yds. 18. A typical airplane will fly at a cruising altitude of A. inches B. feet C. yards D. miles 19. Measure the length of the rectangle using the inch ruler shown. A inches B inches C inches D. 7 8 inches 20. Measure the length of the rectangle using the inch ruler shown. A. 3 4 inches B. 7 8 inches C inches D inches 21. Measure the length of the rectangle using the inch ruler shown. A inches B inches C inches D inches 2

11 ID: A 22. Measure the length of the rectangle using the inch ruler shown. 25. Measure the length of the rectangle using the centimetre ruler shown. A inches B inches C inches D inches A cm B. 3 cm C. 3.5 cm D. 3.9 cm 26. Measure the length of the rectangle using the centimetre ruler shown. 23. Measure the length of the rectangle using the centimetre ruler shown. A cm B. 1 cm C. 1.5 cm D. 1.2 cm A cm B. 3 cm C. 3.5 cm D. 3.2 cm 24. Measure the length of the rectangle using the centimetre ruler shown. A cm B. 2 cm C. 2.5 cm D. 2.3 cm 3

12 ID: A Referents Answer Section 1. B 2. D 3. C 4. A 5. A 6. A 7. B 8. B 9. B 10. A 11. A 12. D 13. B 14. B 15. C 16. A 17. B 18. B 19. B 20. D 21. C 22. A 23. D 24. D 25. D 26. D 1

13 Math 10 C 1.3 SI units and Imperial Units Example 1 Converting from Metres to Feet A. A bowling lane is approximately 19 m long. What is this measurement to the nearest foot? 1900 cm 1 in. 1ft. = 62 ft cm 12 in. B. A Canadian football field is approximately 59 m wide. What is this measurement to the nearest foot? 5900 cm 1 in. 1ft. = 62 ft cm 12 in. Example 2 Converting between Miles and Kilometres A. After meeting in Emerson,Manitoba, Hana drove 62 mi. south and Farrin drove 98 km north. Who drove farther? 62 mi. 1.6 km 1 mi. = 99.2 km Therefore Hana drove farther B. After meeting in Osoyoos, B. C., Takoda drove 114 km north and Winona drove 68 mi. south. Who drove farther? 68 mi. 1.6 km 1 mi. = km Therefore Takoda drove farther

14 Math 10 C Example 3 Solving a Problem that Involves Unit Conversions A. Alex is 6 ft. 2 in. tall. To list his height on his driver s license application, Alex needs to convert this measurement to centimetres. What is Alex s height to the nearest centimetre? = 74 in. 74 in cm 1 in. = 188 cm B. Nora knows that she is 5 ft. 7 in. tall. What height in centimeters will she list on her driver s license application? = 67 in. 67 in cm 1 in. = 170 cm Example 4 Estimating and Calculating Using Unit Conversions A. A truck driver knows that her semitrailer is 3.5 m high. The support beams of a bridge are 11 ft. 9 in. high. Will the vehicle fit under the bridge? Justify the answer = 141 in. 141 in cm 1 in. 358 cm = 3.58 m The semi will fit. = 358 cm B. A truck driver knows that his load is 15 ft. wide. Regulations along his route state that any load over 4.3 m wide must have wide-load markers and an escort with flashing lights. Does this vehicle need wideload markers? Justify your answer. 15 ft. 12 in cm 1m = cm 1 ft. 1 in. 100 cm There will need to be wide-load markers and an escort.

15 ID: A SI and Imperial Units Math 10C Name: 1 mile = 5280 feet 1 yard = 3 feet 1 foot = 12 inches 1 inch = 2.54 cm 1 metre = 3.28 feet 1 mile = 1.6 km 1 pound = kg 1 gallon = 3.79 litres 1 quart = litres in.- inch ft.- feet yd.- yard mi.- mile lb - pound gal - gallon 1. Convert m to feet. 10. Convert 488 feet to m.. 2. Convert 124 miles to km Convert 29 mi. to the nearest kilometre. Use the conversion that 1 mile is about 1.6 km. 12. Convert 89 km to miles. 3. Convert 146 inches to cm Convert 171 m to yards. 4. Convert 342 km to miles Convert 104 inches to cm. 15. Convert 195 cm to feet and the nearest inch. 5. Convert 121 feet to m Convert 32 mi. to the nearest kilometre. Use the conversion that 1 mile is about 1.6 km. 6. Convert 40 cm to inches. 17. Convert 126 cm to feet and the nearest inch.. 7. Convert 77 inches to cm. 8. Convert 171 cm to feet and the nearest inch. 9. Convert 8.3 metres to feet and the nearest inch. 18. Convert 301 miles to km. 19. Convert 8.7 metres to feet and the nearest inch. 20. Convert 395 km to miles. 21. Convert 30 mi. to the nearest kilometre. Use the conversion that 1 mile is about 1.6 km. 1

16 ID: A SI and Imperial Units Answer Section feet m 3.28 feet 1m km 124 miles 1.6 km 1miles cm 146 inches 2.54 cm 1inches miles 342 km 1miles 1.6 km m 121 feet 1m 3.28 feet inches 40 cm 1 inches 2.54 cm cm 8. 5 ft. 7 in ft. 3 in m km miles yards cm ft. 5 in km ft. 2 in km ft. 7 in miles km 1