Relating SI and Imperial Units

Convert between metric and imperial units. Math 10-C Alberta mathematics curriculum.

Lesson 1.2 of Measurement in Math 10C — Alberta curriculum lessons.

What you'll learn in this lesson

• The Conversion Table. Explore the key SI-to-imperial and imperial-to-SI conversions you will use most, and learn how to set up a conversion fraction so unwanted units cancel.
• Single Conversions. Practice converting a single measurement between SI and imperial units, including two-step problems where a mixed measurement must first be turned into one unit.
• Comparing Distances. Learn the strategy for deciding which of two distances given in different units is larger by converting both to the same unit before comparing.
• Comparing Speeds — Multi-Step Conversions. Work through speed problems that require converting both a distance unit and a time unit simultaneously using chained conversion fractions.

Inside the lesson — a free preview

Why Two Systems?

Two Systems, One World. Canada uses SI (metric) units, but the United States uses imperial units. Because we trade, travel, and share media constantly, you will encounter both.

Both systems measure the same thing — length — just with different-sized units. Converting between them works exactly the same way as converting within imperial: multiply by a conversion fraction that equals 1.

Key Conversions

The Two Most Important Conversions. The two relationships you will use most often are:

1 in = 2.54 cm (exact)

1 mi ≈ 1.609 km

If you know just those two, you can derive almost everything else in the table.

How to Use Conversion Fractions

The Cancellation Strategy. Set up the conversion fraction so the unit you want to get rid of is on the bottom of the fraction. That way the unwanted unit cancels out and you are left with the new unit.

For example, to convert 21 m to feet using 1 m = 3.2808 ft:

21 m × (3.2808 ft)/(1 m)

The m on top and bottom cancel, leaving ft as the unit of the result.

Worked example: Bowling Lane

A bowling lane is approximately 21 m long. What is the measurement to the nearest foot?

Solution — Example 1. Given conversion: 1 m = 3.2808 ft

Step 1 — Set up the conversion fraction with metres on the bottom:

21 m × (3.2808 ft)/(1 m) = 68.9 ft

Step 2 — Round to the nearest foot:

Answer: A bowling lane is about 69 ft long.

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