Length conversions using dimensional analysis

Multi-step chain. Pick the right factors so the unwanted units cancel and only the target unit survives.

01 Worked Example Video

Every step of Length conversions using dimensional analysis 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's an example of what you'll see.

Bikeathon distance

As part of an annual fundraiser, Ann joined a bikeathon. The track she biked on was 1,870 yd long. Ann biked 32 laps. How many miles did she bike?

ALEKS gives you a bank of ratios. Pick three and place them in the equation so units cancel down to miles.

▸ Ratios available

3 ft
1 yd

1 yd
3 ft

1870 yd
1 lap

1 lap
1870 yd

5280 ft
1 mi

1 mi
5280 ft

32 laps×××=?miles

answer =

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

Plan the chain: start → intermediates → target each factor cancels one unit

Put the unit you want to cancel on the bottom of the next factor

Dimensional analysis is unit bookkeeping. Line up factors so the previous link’s unit sits on the bottom of the next — canceling it — and the unit you want survives on top. See it live: build a chain in Medium mode →

Common slip

Wrong-direction factor. Picking 1 yd / 3 ft instead of 3 ft / 1 yd puts yards on top, canceling nothing. Always check: the unit you want to cancel goes on the bottom of the next factor. Second slip: skipping a step — going laps → mi directly leaves you stuck. Plan the full path first.

04 Practice — Step by Step

Practice this problem step by step

David walked 20 laps on a 264 yd track. How far did he walk in miles? Use 1 yd = 3 ft and 1 mi = 5,280 ft.

Step 1

Step 1: laps → yards

Multiply 20 laps by the track length. How many yards did David walk?

yards =

Step 2

Step 2: yards → feet

Convert 5,280 yards to feet. Use 1 yd = 3 ft.

feet =

Step 3

Step 3: feet → miles

Convert 15,840 feet to miles. Use 1 mi = 5,280 ft.

miles =

Q8 Q10

Length conversions using dimensional analysis

You walked the 3-factor chain end to end.