Selecting the correct conversion factor

You are not asked to finish the conversion, only to say which factor belongs at one step of it. One rule decides every case: the unit you want gone goes on the bottom.

01 Worked Example Video

Every step of Selecting the correct conversion factor explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE

02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Cancel a top unit

You are converting 18 kilometres into metres:

18 km × [ ? ] = ? m

Type A for 1000 m / 1 km, or B for 1 km / 1000 m.

Cancel a bottom unit

A tap runs at 9 litres per minute and you want litres per hour:

9 L / 1 min × [ ? ] = ? L / hr

Type A for 60 min / 1 hr, or B for 1 hr / 60 min.

Two factors at once

Convert 20 metres per second to kilometres per hour, using 1 km = 1000 m and 1 hr = 3600 s.

Work the chain out and give the speed in km/h.

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 The Rule

put the unit you want to cancel on the bottom it then divides out against the unit above

put the unit you want to keep on the top every factor equals 1, so the value never changes

Both \(\tfrac{5280\ \text{ft}}{1\ \text{mi}}\) and \(\tfrac{1\ \text{mi}}{5280\ \text{ft}}\) are true, and both equal 1. Only one of them cancels the unit you are trying to get rid of, and that is the only thing separating the right choice from the wrong one.

Common slips

(1) Flipped the factor. Both versions look correct because both are correct; only one cancels. Cover the numbers and read the units alone. (2) Forgot the unit being cancelled might be in a denominator. In miles per hour the hours are already on the bottom, so to cancel them the new factor needs hours on top. (3) Tried to do it in one jump. Miles per hour to feet per second is two separate factors; picking one correct factor is the whole question.

04 Practice — Step by Step

Read the units, ignore the numbers

A car travels at 45 miles per hour. We want its speed in feet per second, using 1 mi = 5280 ft and 1 hr = 3600 s.

The chain looks like this:

45 mi / 1 hr × [ ? ] × [ ? ] = ? ft / s

Step 1

Cancel the miles

Miles are on the top of 45 mi / 1 hr. Which factor cancels them and leaves feet?

Step 2

Cancel the hours

Hours are on the bottom of 45 mi / 1 hr. Which factor cancels them and leaves seconds?

Step 3

Now finish it

45 × 5280 ÷ 3600. What is the speed in feet per second?

Q14 Q16

Selecting the correct conversion factor

Why ALEKS stops at the choice