3.2 Converting Measurements

Transcription

1 1 3.2 Converting Measurements We need to be able to convert metric measurements to larger or smaller metric measurements. In addition, since we live close to the United States we need to know how to convert units from imperial units to larger or smaller imperial units. Finally, we need to convert metric to imperial and vice versa. A. Converting Metric Units: Recall that the most common metric units of length used are the kilometre (km), the metre (m), the centimetre (cm) and the millimetre (mm). These units of length are related as follows: 10 mm = 1 cm 100 cm = 1 m 1000 m = 1 km To convert length from a larger unit into a smaller unit, multiply by the relevant power of 10. To convert length from a smaller unit into a larger unit, divide by the relevant power of 10. Examples: Convert the following measurements to the indicated units: a) 7 cm to mm b) 8 m to cm c) 9000 m to km d) 2.5 m to mm Worksheet: Converting Metric Units

2 2 Converting Metric Units Worksheet Convert the following measurements to the units indicated: a) 25 m to cm g) 8.26 m to mm b) 6 m to mm h) 4.75 km to mm c) 4 km to cm i) 975 m to km d) 3 km to mm j) 650 cm to m e) 62.8 cm to mm k) 8000 mm to m f) 48.7 m to cm l) cm to km Answers: a) 2500 cm b) 6000 mm c) cm d) mm e) 628 mm f) 4870 cm g) 8260 mm h) mm i) km j) 6.5 m k) 8 m l) 9.5 km

3 3 B. Converting Imperial Units To convert imperial units, you must use a conversion factor. A unit conversion factor is a fraction that is equal to 1. The numerator (top) of the fraction contains the units of the unit you want to convert to. Table of Conversions: 12 inches = 1 foot 36 inches = 1 yard 5280 feet = 1 mile 1760 yards = 1 mile 1 inch = 2.54 cm 1 foot = 30.5 cm 1 foot = 0.305m 1 yard = 3 feet 1 yard = 0.915m 1 mile = 1.6km Whenever we do conversions it s important to put whatever we want we put on top and whatever we have we put on the bottom. Example 1: Convert 116 inches to feet. Example 2: Convert 25 miles to yards.

4 4 Practice: 12.5 inches x. 76 cm x. 7 yards x 149 inches x 20 ft x Worksheet: Converting Imperial Units Converting Imperial Units Worksheet Convert the following measurements to the indicated units to 2 decimal places. a) 5 cm to inches b) 15 m to feet

5 5 c) 10 m to yards i) 3 feet to centimetres d) 10 km to miles j) 2 yards to meters e) 20 feet to meters k) feet to miles f) 25 yards to meters l) 5 feet 8 inches to inches g) 10 feet to meters m) 2000 yards to miles h) 100 km to miles n) 200 miles to km Answers: a) 1.97 in b) ft c) yd d) 6.22 mi e) 6.10 m f) m g) 3.05 m h) mi i) cm j) m k) 5.68 mi l) 68 in m) 1.14 mi n) km

6 6 C. Converting Units Word Problems Many everyday situations require conversions between units. Trades, industry, and many businesses will convert units on a daily basis. Examples: 1) Mary is delivering a load of goods from Vancouver BC to Seattle WA, and then in Seattle she is picking up another load to deliver to Albuquerque, NM. The distance from Vancouver to Seattle is 220 km and the distance from Seattle to Albuquerque is 1456 mi. The odometer in Mary s truck records distance in kilometers. a) What is the total distance she will travel in kilometers? b) If her odometer read km when she left Seattle, what did it read when she left Vancouver? c) What will her odometer read when she reaches Albuquerque?

7 7 2) Mark owns a carpet store and sells hallway runners for $9.52/linear foot. a) How much is this per linear yard? b) How much is the per linear metre? c) Ralph needs 3.9 m of the runner for his hallway. How much will it cost? Converting Units Word Problem Worksheet Converting Units Word Problem Worksheet 1) Suzanne purchased tiles for her patio that are 8 by 4. She measured her patio in metres and wants to convert the tile dimensions to SI units. What are the dimensions of the tiles in centimeters? 2) Ben owns an older American truck. The odometer shows distance travelled in miles. On a recent trip to deliver produce for his employer, he drove 1564 miles. His employer pays him $0.89/km for the use of his own truck. How much will he be reimbursed for the use of his truck for the trip?

8 8 3) A school custodian must mark off a field that is 150 ft by 85 ft. His tape measure is marked in metres. What are the dimensions of the field in metres (to the nearest tenth of a metre)? 4) Jeff knows that his semi-trailer truck is 3.3 m high. A tunnel is marked as Max height: Will Jeff s truck fit through the tunnel? 5) Carla needs 3.5 m of cloth. If the cloth she wants to purchase costs $9.78/yd, how much will the cloth cost? 6) John is a picture framer. He is framing a picture that is 24 inches by 32 inches with a frame that is 2.5 inches wide. What is the outer perimeter of the framed picture: a) In inches? b) In feet and inches? c) In yards, feet, and inches? Answers: 1) 20.3 cm by 10.2 cm 2) $ ) 45.7 m by 25.9 m 4) no too tall 5) $ ) a) 132 in b) 11 ft c) 3 yd 2 ft

9 9 Converting Units Review Worksheet 1. Convert the following imperial measurements: a) 42 inches to feet d) 5 miles to yards b) 84 inches to yards and feet e) 6 feet to inches c) 96 inches to yards f) 1.2 yards to inches 2. Convert the following metric measurements. Recall: a) 5000 metres to kilometres c) 65 centimetres to metres b) 25 centimetres to millimetres d) 150 millimetres to centimetres

10 10 3. Convert the following measurements. a) 16 feet to metres d) 220 yard to meters b) 120 metres to yards e) 45 miles to kilometers c) 26 inches to centimeters f) 150 centimeters to feet 4. Charlie drove from Calgary to Saskatoon, which is a distance of 620 km. How far is this in miles?

11 11 Answers: 1) a) 3.5 ft b) 2 yd 1 ft c) 2.67 yd d ) 8800 yd e) 72 in f) 43.2 in 2) a) 5 km b) 250 mm c) 0.65 m d) 15 cm 3) a) 4.88 m b) yd c) cm d) m e) km f) 4.92 ft 4) miles 3.2 Quiz