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E. Geometry and Measurement · Geometry and Measurement: Circles, Triangles, Measurement Systems, Pythagoras and Volume

Converting Between Measurement Systems, Including Units from Different Communities

E1.3 A1 A2About 75 minutes
Learning goals
  • I can convert between metric and imperial units of length, area, mass, capacity and temperature.
  • I can choose whether to use an exact equivalent (1 in = 2.54 cm) or a rounded one, and round my answer sensibly.
  • I can solve problems with units used by different communities and in Canadian history, such as the arpent and the surveyor's chain.
  • I can use a formula or a spreadsheet to do many conversions at once.

Words to know

equivalent
A value in one unit that equals a value in another unit, like 1 in = 2.54 cm.
exact equivalent
An equivalent that is true by definition, with no rounding: 1 in = 2.54 cm exactly.
arpent
A French unit used in New France and still found in some Québec land descriptions. A linear arpent is about 58.5 m.
chain (Gunter's chain)
A surveyor's unit of 66 ft (about 20.1 m). 80 chains = 1 mile, and 10 square chains = 1 acre.
acre
An imperial unit of land area: 43 560 ft², about 0.405 ha.
degree Fahrenheit (°F)
A temperature unit. Water freezes at 32 °F and boils at 212 °F at sea level.

A hook: Canada speaks two measurement languages

The road sign says 100 km/h, but your cousin from Michigan reads speeds in miles per hour. Your doctor records your height in centimetres, but your friend says she is 5 ft 4 in. The hockey rink is 200 ft long. A recipe says to bake at 350 °F.

Canadians switch between systems all the time. Today you will learn to do it accurately.

QuantityKey equivalents (≈ means rounded)
Length1 in = 2.54 cm (exact); 1 ft = 30.48 cm (exact); 1 yd = 0.9144 m (exact); 1 mi ≈ 1.609 km
Area1 ft² ≈ 0.0929 m²; 1 acre ≈ 0.4047 ha; 1 mi² ≈ 2.59 km²
Mass1 lb ≈ 0.4536 kg (about 454 g); 1 kg ≈ 2.205 lb; 1 oz ≈ 28.35 g
Capacity1 imperial gallon ≈ 4.546 L; 1 US gallon ≈ 3.785 L
Temperature°F = 1.8 × °C + 32; °C = (°F − 32) ÷ 1.8
Equivalents between imperial and metric. Use the exact ones when you can, and round only at the end.
0123450123456789101112inchescm1 in = 2.54 cm
A ruler with both scales. One inch (top) lines up with 2.54 cm (bottom), so 5 in = 12.7 cm.

Two strategies

  1. Conversion factors: 69 in × (2.54 cm / 1 in) = 175.26 cm. The units cancel.
  2. Proportions or double number lines: if 1 in ↔ 2.54 cm, then 69 in ↔ 69 × 2.54 cm.

For temperature, the scales do not start at the same zero, so we need a formula, not just a multiplier.

−40 °C−40 °F−40 °C = −40 °F0 °C32 °Fwater freezes20 °C68 °Froom temperature37 °C98.6 °Fbody temperature100 °C212 °Fwater boils (sea level)CelsiusFahrenheit
The Celsius and Fahrenheit scales side by side. Each Celsius degree equals 1.8 Fahrenheit degrees, and 0 °C lines up with 32 °F. At −40 the two scales give the same number.
Worked example

Example 1: Height

Leo is 5 ft 9 in tall. What is his height in centimetres?

  1. Change to inches: 5 × 12 + 9 = 69 in.
  2. 69 in × 2.54 cm/in = 175.26 cm.
  3. Round sensibly: about 175 cm.

175.26 cm, about 175 cm

Worked example

Example 2: The rink

An NHL-size rink is 200 ft by 85 ft. Find its area in m².

  1. Change each length first: 200 ft × 0.3048 m/ft = 60.96 m and 85 ft × 0.3048 = 25.908 m.
  2. A = 60.96 × 25.908 ≈ 1579.4 m².
  3. Check another way: A = 200 × 85 = 17 000 ft², and 1 ft² = 0.3048² m² ≈ 0.0929 m², so 17 000 × 0.0929 ≈ 1579 m². ✓

About 1579 m²

Worked example

Example 3: Oven temperature

A recipe says 350 °F. What is that in °C?

  1. °C = (°F − 32) ÷ 1.8.
  2. (350 − 32) ÷ 1.8 = 318 ÷ 1.8 ≈ 176.7.
  3. Most ovens in Celsius use steps of 5 or 10 degrees, so set it to about 175 °C or 180 °C.

About 177 °C

Units from Canadian communities and history

  • The arpent. In New France, land along the St. Lawrence River was divided into long lots: narrow strips that each touched the river, which was the main road. Lots were measured in arpents (a linear arpent is about 58.5 m), and you can still find arpents in some Québec property descriptions.
  • River lots. Métis families along the Red River in what is now Manitoba also farmed long, narrow river lots. In 1869 Canadian surveyors arrived to lay out a square grid instead, and Métis people led by Louis Riel stopped the survey. Measurement was tied to land, community and rights.
  • The surveyor's chain. Much of Canada, including the Prairies, was surveyed with Gunter's chain: 66 ft long, with 100 links. 80 chains make 1 mile, and 10 square chains make 1 acre. The Dominion Land Survey divided land into townships of 36 square sections, each 1 mile on a side.
riverlong, narrow lotseach touches the riverLong lots (river lots)Square survey township1 section =1 mi × 1 mi= 640 acres36 sections = 6 mi × 6 mi(schematic, not to scale)
Two ways to divide land. Long lots give every family river frontage. A square grid of 1-mile sections ignores rivers and hills. The units used shaped how communities lived.
Worked example

Example 4: A long lot

A lot is 3 arpents wide and 30 arpents deep. Using 1 arpent ≈ 58.5 m, find its area in hectares.

  1. Width: 3 × 58.5 = 175.5 m. Depth: 30 × 58.5 = 1755 m.
  2. A = 175.5 × 1755 ≈ 308 000 m².
  3. 1 ha = 10 000 m², so 308 000 ÷ 10 000 ≈ 30.8 ha.

About 30.8 ha (a long, thin farm: 10 times longer than wide)

Worked example

Example 5: A section of land

One section is 640 acres. Convert to hectares.

  1. 640 acres × 0.4047 ha/acre ≈ 259 ha.
  2. Check: 1 mi² ≈ 1.609 km × 1.609 km ≈ 2.59 km² = 259 ha. ✓

About 259 ha

Technology: a conversion spreadsheet

In a spreadsheet, put inches in column A. In B2 type **=A22.54 and fill down to get centimetres for the whole column. For temperatures, type =(A2-32)/1.8*. Spreadsheets are perfect when you have a long list, like a team roster of heights.

Watch out!

  • Round only at the end. Rounding 0.3048 to 0.3 makes a 200 ft rink about 1.6% too short.
  • Imperial and US gallons are different: an imperial gallon is about 4.546 L, a US gallon about 3.785 L.
  • Temperature needs the full formula. 20 °C is not 20 × 1.8 = 36 °F; it is 36 + 32 = 68 °F.
Hands-on activity

Label detective

You need: food packages or cans, a measuring tape with both scales, a calculator.

  1. Find 3 packages that show both metric and imperial amounts (for example "454 g (1 lb)"). Check each with 1 lb ≈ 454 g or 1 oz ≈ 28.35 g. Are they rounded?
  2. Measure the height of everyone at home in cm. Convert to feet and inches. (Divide by 2.54 to get inches, then by 12.)
  3. Check tonight's weather forecast in °C and convert the high and low to °F.

Model answer: 160 cm ÷ 2.54 ≈ 63 in = 5 ft 3 in.

Just for fun

−40 is the only temperature where Celsius and Fahrenheit agree. In a Canadian cold snap, it is also the only temperature where everyone agrees it is too cold to go outside.

Your turn

1

Convert 12 in to centimetres.

2

Convert 50 km to miles, to one decimal place.

3

A baby has a mass of 8 lb. What is that in kilograms, to two decimals?

4

Convert 25 °C to °F.

5

How many litres are in 10 imperial gallons?

6

A CFL field is 110 yd long between goal lines. How long is that in metres?

7

How long are 2 chains in metres?

More practice: warm-up

1

1 in = ? cm

2

About how many pounds are in 1 kg?

3

Water boils at 100 °C at sea level. What is that in °F?

4

About how many kilometres are in 1 mile?

5

3 ft = ? m

More practice: on your own

1

A recipe needs 2 lb of flour. How many grams is that, to the nearest gram?

2

A sign says 80 km/h. What is that in miles per hour, to one decimal?

3

Convert −10 °C to °F.

4

A "2 by 4" piece of lumber is actually 1.5 in by 3.5 in. Give these sizes in millimetres.

5

1 acre = 43 560 ft². How many square metres is that?

Challenge

1

A can of paint covers 400 ft². A room's walls have an area of 30 m². Is one can enough for two coats?

2

A marathon is 42.195 km. How many miles is that, to two decimals? Use 1 mi = 1.609 344 km.

3

Use chains to show that 1 square mile = 640 acres.

Check your understanding

Quiz

1.

Which equivalent is exact?

2.

Convert 30 °C to °F.

3.

Mia is 5 ft 2 in tall. About how tall is she in cm?

4.

A lot is 2 arpents wide and 20 arpents deep (1 arpent ≈ 58.5 m). About how deep is it?

5.

Which is true about gallons?

6.

How many acres are in one section of the Dominion Land Survey?

For parents and teachers

Big idea: Expectation E1.3 asks students to convert between measurement systems, including units from various cultures and communities. In Canada the metric and imperial systems live side by side, and historical units like the arpent and surveyor's chain still shape property lines today.

Common difficulties:

  • Multiplying vs dividing. Ask: "Is a centimetre bigger or smaller than an inch? So should the number get bigger or smaller?"
  • Temperature. Students often forget the + 32 or − 32. Use 0 °C = 32 °F as a check.
  • Rounding too early. Keep the full equivalent until the last step.

How to help: Shopping flyers, recipes, weather apps and sports (football yards, hockey rink feet) give real conversions. Ask your teen to convert one thing a day. If your family has its own traditional units (from another country or community), share them; comparing them to metric is exactly what this expectation asks.