Unit 2 Measurements and Conversions...Apprenticeship and Workplace Math 10 Unit 2 – Measurements and Conversions 8 2. Express each measurement in feet. a) 7 yd, 2 ft b) 12 yd, 1

Apprenticeship and Workplace Math 10

Name: ________________________________________________________________________________ Block: ______________

Unit 2 – Measurements and Conversions

2.1 Reading Rulers 2.2 Metric Length Conversions 2.3 Imperial Length Conversions 2.4 Metric/Imperial Length Conversions 2.5 Mass Conversions 2.6 Volume/Capacity Conversions

Apprenticeship and Workplace Math 10 Unit 2 – Measurements and Conversions

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2.1 – Reading Rulers The SI System (or Système International d’Unités) is known as the metric system. This system was

developed in France in 1791 to standardize all types of measurements around the world. The base

metric unit for length is the metre. All other metric length units are written in terms of this base unit:

1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm

Rulers and tape measures that use the metric system divide a metre into 100 parts and a centimetre into 10 parts: The imperial system evolved from a system used in ancient Rome based on referents from the human body and everyday activities. For example,

• 1 inch—the width of a person’s thumb • 1 foot—the distance from a person’s heel to the big

toe • 1 yard—the length of a person’s stride

Often these units were based on an important person, like a king. This resulted in units that were different in different regions. In 1824, the units were standardized and became the imperial system. Rulers and tape measures that use the imperial system divide an inch into 16 parts. This means working with fractions: Examples


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Ex 1. Write the measurement indicated by each arrow on these metric rulers. Express your answer in both centimetres and millimetres.

a)

b) Ex 2. Write the measurement indicated by each arrow on these imperial rulers. Express your answer

in inches.

a) b)

c)


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Ex 3. Write the measurement indicated on these tape measures. Express your answer in both feet/inches as well as just inches.

a)

b) 2.1 Practice

1. Write the measurement indicated by each arrow on these metric rulers. Express your answer in both centimetres and millimetres.

a)

____________ cm or ____________ mm

b) ____________ cm or ____________ mm


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2. For the following imperial ruler:

a) Find length A in inches

b) Find length B in inches

c) Find length C in inches

3. For the following imperial measuring tape:

a) Find the length of D in both feet, inches and just inches.

_________ feet, _______________ inches or _________________ inches

b) Find the length of E in both feet/inches and just inches.

_________ feet, _______________ inches or _________________ inches


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2.2 Metric Length Conversions

We can use the unit cancellation method to convert between metric

units of length.

Examples

Ex 1. Convert 5 m to cm Ex 2. Convert 10.36 cm to m

Ex 3. Convert 2.4 m to mm

Ex 4. Convert 523 000 cm to km

2.2 Practice

1. Complete each measurement in the given units:

a) 25 km to m b) 12.5 cm to m

c) 7856 m to km d) 0.045 m to mm

e) 6500 cm to km f) 65 m to mm

1 km = 1000 m 1 m = 100 cm

1 cm = 10 mm


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2. A tree house is built 2.4 m off the ground. How many steps are required to reach the tree

house if the steps are placed 20 cm apart?

3. Photocopy paper is 0.1 mm thick. A package contains 500 sheets. What is the thickness of the

package, in centimetres?

4. At the high school track meet, Cecilia ran the 800 m race, the 5000 m race and the 10 000 m

race. How many kilometres did she run altogether?

5. Nora is a buyer for a floor tiling company. She needs 190 tiles for a project. She finds a stack

that she estimates to be about 2 m high. If each tile is 1.2 cm thick, are there enough tiles in

the stack for her project?

6. Jim needs to buy enough baseboard to run the 18.6 m perimeter of a room. Each piece of

baseboard is labelled to be 300 cm long. How many does Jim need to buy?


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2.3 Imperial Length Conversions

We can again use the unit cancellation method to convert between

imperial units of length.

Examples

Ex 1. Convert 21 ft to yd Ex 2. Convert 5 yd to in

Ex 3. Colin is 5 ft, 11 in tall. How tall is he in inches?

Ex 4. Express 2 mi, 3 yd in feet. 2.3 Practice

1. Express each measurement in inches.

a) 2 yd b) 51

2 yd

c) 6 ft, 2 in d) 4 ft, 9 in

e) 3 yd, 1 ft f) 5 yd, 2 ft, 3 in

1 mi = 1760 yd 1 yd = 3 ft 1 ft = 12 in


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2. Express each measurement in feet.

a) 7 yd, 2 ft b) 12 yd, 1 ft

c) 2 mi d) 3 mi, 5 yd, 1 ft

3. Ray is building a fence using panels that are sold in 8 ft lengths. The perimeter of his backyard

measures 32 yd. How many fence panels should he buy?

4. Riley bought 59 feet of rope. He cut off pieces that total 34 feet, 8 inches in length to use as tie-

downs on his boat. How much rope does he have left, in feet and leftover inches?

5. The Olympic marathon is a running race that is 26 mi, 385 yd long. If Sebastian’s stride is

about 1 yd long, how many strides will he take in the marathon?


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2.4 Metric/Imperial Length Conversions It is useful to be able to convert imperial units of length to metric, and vice versa. Examples Ex 1. How many kilometres is 436 miles? Round to the nearest tenth. Ex 2. A soccer goal is 24 ft wide. About how wide is it in metres? Round to the nearest tenth. Ex 3. Andrea's height is 5 ft, 7 in. What is her height, to the nearest centimetre? Ex 4. Rob’s height on his driver’s licence is 185 cm. About how tall is he is feet and leftover inches? Ex 5. The diameter of a spark plug is 14 mm. What is this measure in inches? Round to the nearest

hundredth.

1 mi ≈ 1.609 km 1 yd = 0.9144 m 1 ft = 30.48 cm 1 in = 2.54 cm


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2.4 Practice

1. Find the greater measurement in each pair. a) 6 in or 10 cm b) 5 ft or 125 cm

c) 10 yd or 10 m d) 60 mm or 2 in

2. Express each measurement in centimetres. Round your answers to the nearest tenth.

a) 8 in b) 16 3

4 in

c) 2 ft, 3 1

2 in d) 4 yd

3. The tallest man ever recorded was 2.72 m. What was his height in feet and leftover inches?


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4. Express each measurement in metres. Round to the nearest hundredth.

a) 12 ft b) 6 yd 2 ft

5. A standard piece of paper has dimensions 8 1

2 in by 11 in. What are its dimensions in

centimetres?

6. Express each measurement in kilometres. Round your answers to the nearest hundredth.

a) 9.5 mi b) 1 mi 200 yd

7. Marie is a long distance runner. Her next race is 10 000 m. How far will she run in miles? Round to the nearest tenth.

8. The Capilano suspension bridge near Vancouver is 140 m long. What is its length in feet?

Round to the nearest tenth.


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2.5 Mass Conversions

The mass of an object refers to the quantity of matter in it, and it remains constant, no matter where the object is located.

In the metric system, the kilogram is the basic unit of mass. We also use its derivatives: grams, milligrams and metric tonnes. The basic unit of mass in the imperial system is the pound, but we also have tons and ounces.

Examples Ex 1. Convert the following:

(a) 5½ lb to oz (b) 2.4 kg to g

(c) 800 lb to imperial tons (d) 22 150 kg to metric tonnes

Ex 2. Manuela needs 1 pound 2 ounces of Gruyère cheese, 12 ounces of cheddar cheese, and 10 ounces of Swiss cheese for a fondue recipe. How many pounds of cheese does she need in all?

Imperial Imperial to Metric Metric

1 T = 2000 lb 1 lb = 16 oz

Abbreviations:

ton (imperial) = T pound = lb ounce = oz

1 T ≈ 907 kg 2.2 lb ≈ 1 kg 1 lb ≈ 454 g

1 oz ≈ 28.35 g

1 t = 1000 kg 1 kg = 1000 g 1 g = 1000 mg

Abbreviations:

tonne (metric) = t kilogram = kg

gram = g milligram = mg


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Ex 3. Lorinda is baking apple pies. According to her recipe, she needs 6 pounds of apples. The bag of apples she bought only shows the mass in kilograms. How many kilograms of apples does she need? Ex 4. A baby boy had a mass of 7 pounds 12 ounces at birth. What was his mass in kilograms? 2.5 Practice

1. Convert:

a) 22 oz to pounds b) 7890 lb to tons

c) 54 oz to pounds and leftover ounces d) 6 lb, 2 oz to ounces

2. Kris needs to transport 5 slabs of concrete to an apartment work site. If each slab has a mass of 46

pounds, Kris is 195 pounds, and the truck is 1.5 tons, what is the total mass of the loaded truck in pounds?


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3. A bakery uses a recipe for oatmeal cookies that calls for 1 lb 5 oz of flour to make 9 dozen cookies. How many ounces of flour are needed to make 3 dozen cookies?

4. Convert the following masses.

a) 2.5 t to kilograms b) 2.8 kg to grams

c) 125 g to kilograms d) 2.4 g to milligrams

5. What is the total mass of a loaded truck if the truck has a mass of 2.6 tonnes and it is loaded with

15 skids of boxes that are 210 kilograms each? Express your answer in metric tonnes. 6. Irene needs 1.6 kg of tomatoes to make her grandmother’s recipe for ratatouille. She has baskets

of tomatoes that weigh 256 g, 452 g, 158 g, and 320 g. How many more grams of tomatoes does she need?


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7. Karen is making a batch of potato soup. If she needs 6.5 lb of potatoes, and each potato weighs about 375 g, about how many potatoes does she need?

8. Alphonse is making chicken kebabs for 14 people. His recipe suggests about 7 oz of chicken per

person. At the grocery store, the mass of chicken is labelled in kilograms. How many kilograms of chicken does Alphonse need to buy? Round to the nearest tenth.

9. A sign posted in an elevator says “Maximum capacity 1400 lb.” If the average mass of an adult is

80 kg, about how many adults can the elevator carry?


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2.6 Volume/Capacity Conversions

The capacity of a container is the amount it can hold; in other words, its volume.

Capacity is often used with liquid measures. In the metric system, the basic unit of capacity is the

litre. In the imperial system, we use units such as gallons, quarts, pints, cups, and fluid ounces.

Most recipes have ingredient amounts written in imperial units.

Imperial Imperial to Metric Metric

1 gal = 4 qt 1 qt = 2 pt 1 pt = 2 c

1 c = 8 fl oz 1 fl oz = 2 tbsp 1 tbsp = 3 tsp

Abbreviations:

gallon = gal quart = qt pint = pt cup = c

fluid ounce = fl oz tablespoon = tbsp or T

teaspoon = tsp or t

1 gal ≈ 3.79 L 1 qt ≈ 946 mL

1 fl oz ≈ 29.57 mL 1 fl oz = 2 tbsp 1 tbsp ≈ 15 mL

1 L = 1000 mL

Abbreviations: litre = L

millilitre = mL

Examples Ex 1. Jayme is making a punch for a party. The recipe calls for 72 fl oz of pineapple juice, and 4.5 quarts of orange juice.

a) How many cups of pineapple juice does she need?

b) How many litres of orange juice does she need? Round to the nearest tenth.


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Ex 2. Paula is following a crème brulée recipe written in metric units, but she has imperial measuring devices. The recipe requires 500 mL of cream and 1.25 mL of vanilla.

a) About how much cream will she need, in cups?

b) How much vanilla will she need, in teaspoons?

2.6 Practice 1. Convert the following capacities to the units indicated. Round to the nearest tenth when needed.

a) 16 pints = _____ cups = _____ quarts b) 3 fl oz = ______ T (tablespoons)

c) 4 gal = _______ pt d) 5.64 L = ___________mL

e) 560 gal = __________ L f) 56 quarts = __________ L


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2. If a 1 gal jug of milk and a 4 L jug of milk are the same price, which jug should you choose? Explain. 3. A can of diced tomatoes is 28 fl oz. Sarah needs 7 cups of diced tomatoes for the soup she is making. How many cans does she need? 4. Serina is travelling through the US and her car's gas tank has a capacity of 55 litres.

a) What is this capacity in gallons? Round to the nearest hundredth.

b) If gas costs $2.99/gal in Bellingham, Washington, how much will it cost to fill her car (assuming that it is totally empty)?


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ANSWERS

Section 2.1

1. a) 8.4 cm or 84 mm b) 13.9 cm or 139 mm

2. a) 1

2 in.

b) 23

8 in.

c) 33

4 in.

3. a) 3 feet, 101

4 inches or 46

1

4 inches

b) 4 feet, 33

8 inches, or 51

3

8 inches

Section 2.2 1. a) 25 000 m b) 0.125 m c) 7.856 km d) 45 mm e) 0.065 km f) 65 000 mm 2. 12 steps 3. 5 cm 4. 15.8 km 5. About 167 tiles, so not enough. 6. 7 baseboards Section 2.3 1. a) 72 in b) 198 in c) 74 in d) 57 in e) 120 in f) 207 in 2. a) 23 ft b) 37 ft c) 10 560 ft d) 15 856 ft 3. 12 panels 4. 24 ft, 4 in 5. 46 145 strides

Section 2.4 1. a) 6 in

b) 5 ft c) 10 m d) 60 mm

2. a) 20.3 cm b) 42.5 cm c) 69.9 cm d) 365.8 cm 3. 8 ft, 11 in 4. a) 3.66 m b) 6.10 m 5. 21.59 cm by 27.94 cm 6. a) 15.29 km b) 1.79 km 7. 6.2 mi 8. 459.3 ft

Section 2.5 1. a) 1.375 lb b) 3.945 T c) 3 lb, 6 oz d) 98 oz 2. 3425 lb 3. 7 oz 4. a) 2500 kg b) 2800 g c) 0.125 kg d) 2400 mg 5. 5.75 t 6. 414 g 7. About 8 potatoes 8. 2.8 kg 9. 8 adults Section 2.6 1. a) 32 cups; 8 quarts b) 6 T c) 32 pt d) 5640 mL e) 2122.4 L f) 53.0 L 2. By the 4 L jug, since you get more milk for the same price.

3. 2 cans 4. a) 14.51 gal b) $43.38

Documents

Unit 2 Measurements and Conversions...Apprenticeship and Workplace Math 10 Unit 2 – Measurements and Conversions 8 2. Express each measurement in feet. a) 7 yd, 2 ft b) 12 yd, 1