Chain the move.
When one factor isn't enough, stack several. Each one cancels a unit until what's left matches your target. Same recipe as Lesson 4, scaled up.
You see 130 km/h on a German Autobahn sign and want to know how fast that is in mph. Or someone runs an 8-minute mile and you want it as miles per hour. Or you swap 50 USD for British pounds, going USD to EUR to GBP.
One conversion factor isn't enough. You need to chain two or three together, each one canceling a unit until the only thing left is your target. Same recipe as Lesson 4, just stacked.
Stack the factors. Cancel along the chain.
5 mi × (5280 ft / 1 mi) × (12 in / 1 ft) = 316,800 in. Two factors, three units cancel in pairs, only "in" comes out the other side.
A conversion chain is a multiplication of two or more conversion factors, each one set up so that its denominator cancels the numerator of the previous link.
The vocabulary you'll see in word problems
- Chain Two or more conversion factors multiplied in a row. Cancellation propagates link by link until the surviving unit matches the target.
- Compound unit A unit that's a ratio of two units: mph (miles/hour), $/gal (dollars/gallon), kg/L (kilograms/liter). Convert the top and the bottom separately.
- Currency conversion Just unit conversion with money. The exchange rate IS the conversion factor. 1 USD = 0.92 EUR means the factor is 0.92 EUR / 1 USD.
- Temperature exception Fahrenheit and Celsius don't convert with the multiply-by-1 trick because the two scales have different zero points. Use the explicit formulas: C = (5/9)(F − 32) and F = (9/5)C + 32. The subtraction/addition is what handles the offset.
Convert 5 miles to inches.
"You ran 5 miles. How many inches is that? Use 1 mile = 5280 feet and 1 foot = 12 inches."
Plan the chain.
Start unit is mi, target unit is in. There's no direct mi → in factor, but you know mi → ft (5280) and ft → in (12). Stack them.
Set up the first factor.
Cancel the mi from "5 mi" by putting mi on the bottom of the first factor, ft on top.
Set up the second factor.
Cancel the ft that survived the first factor by putting ft on the bottom of the next factor, in on top.
Cancel the units along the chain.
Two pairs cancel: mi in the start meets mi in the first factor's denominator, ft in the first factor's numerator meets ft in the second factor's denominator. Only in is left.
Multiply the numbers.
5 × 5280 × 12. Run the arithmetic.
Three problems. Two-step chains, compound units, and currency.
Convert 2 hours to seconds. (1 hr = 60 min, 1 min = 60 sec.)
Convert 60 mph to ft/sec. (1 mi = 5280 ft, 1 hr = 3600 sec.)
Convert 50 USD to GBP via the euro. (1 USD = 0.92 EUR, 1 EUR = 0.87 GBP.) Round to two decimals.
Three fast questions before you move on.
Q1. In the chain 5 mi × (5280 ft / 1 mi) × (12 in / 1 ft), what unit will the final answer be in?
Q2. When converting 60 mph to ft/sec, you need to...
Q3. Why does cancellation work in a chain?
Three places chains show up.
Once you can chain conversion factors, three common scenarios become routine.
In ALEKS, multi-step conversion problems are common in Topic 2. The trick: identify your start unit and target unit first, then plan the chain on paper before running any numbers. "Mi to in" is two factors. "Mph to m/s" is three. Knowing the path saves time.
In Excel, chain factors stay in their own cells. A formula like =A2*$B$1*$B$2 applies the same chain to every row of data, with the conversion rates anchored by absolute references. That's the pattern Major Assignment 1 will lean on for unit-conversion rows.
Next: Lesson 06 brings percent and conversions back to your own money. Income, expenses, savings rate, and a budget you'll actually use. The on-ramp to MA1.
Continue to Lesson 06Different angle? Need another rep? These are optional — tap any that look helpful.
Unit conversions within the metric system
Sal Khan walks through metric-to-metric conversions step by step (kg → g → mg style). Same chain recipe from the lesson, applied to the metric system specifically. Pairs well with ALEKS Q3's multi-factor setup.
Convert Fahrenheit to Celsius
The temperature exception, walked through carefully. Same formulas as the lesson's pitfall callout, with extra examples. Useful prep for ALEKS Q6 (the Moscow temperature problem).