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Math

Unit Conversion

4 min readEasy10-question checkpoint

Unit conversion problems test whether you can multiply by the right *fraction* — one that cancels the unit you don't want and leaves the unit you do.

Where this lesson fits

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Ratios and Proportions→

Unit Conversion

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Converting units = multiplying by a conversion fraction equal to 1.

1 hour = 60 minutes, so $\frac{60 \text{ min}}{1 \text{ hr}} = 1$ and $\frac{1 \text{ hr}}{60 \text{ min}} = 1$ . Multiplying by either doesn't change the value — but it does change the units.

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Setting up a conversion fraction — what cancels what

Have	Want	Right fraction	Why
miles	feet	$\times \frac{5280 \text{ ft}}{1 \text{ mi}}$	miles cancels; feet remains
feet	miles	$\times \frac{1 \text{ mi}}{5280 \text{ ft}}$	feet cancels; miles remains
hours	minutes	$\times \frac{60 \text{ min}}{1 \text{ hr}}$	hr cancels; min remains
minutes	hours	$\times \frac{1 \text{ hr}}{60 \text{ min}}$	min cancels; hr remains

The dimensional analysis technique — write everything as a chain of fractions, cancel the units you don't want.

Convert 5 miles to feet (5,280 feet per mile):

5 \text{ mi} \cdot \frac{5280 \text{ ft}}{1 \text{ mi}} = 26{,}400 \text{ ft}

The miles cancel; feet remain. The numerical answer is $5 \times 5280 = 26{,}400$ .

Multi-step conversions. Chain the fractions.

Convert 90 km/h to m/s:

\frac{90 \text{ km}}{1 \text{ hr}} \cdot \frac{1000 \text{ m}}{1 \text{ km}} \cdot \frac{1 \text{ hr}}{3600 \text{ s}} = \frac{90 \cdot 1000}{3600} = 25 \text{ m/s}

The km cancels with km; hr cancels with hr. We're left with m/s.

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Chaining a multi-step conversion

Is the conversion direct (one step), or do you need an intermediate unit?

Yes ↓

→ One fraction. Set it up so the unit you have cancels with the same unit on the bottom.

No ↓

Do you have a chain of facts (e.g., A→B and B→C)?

Yes ↓

→ Multiply both fractions in series: A → B → C. Each step cancels the previous unit.

No ↓

→ Re-read — find the conversion factor the SAT gave you

SAT-typical setups:

Time conversions: 1 hr = 60 min = 3,600 s. 1 day = 24 hr = 1,440 min.
Length: 1 mile = 5,280 ft = 1,609 m. 1 km = 1,000 m. 1 m = 100 cm.
Volume: 1 gallon ≈ 3.785 L. 1 L = 1,000 mL.
Mass / weight: 1 kg = 1,000 g = 2.205 lb (often approximated).

The SAT often gives you the conversion factor in the problem — you don't need to memorize obscure ones. Read the problem carefully.

Square / cubic units. Converting square or cubic units requires squaring or cubing the linear factor.

1 m = 100 cm. So 1 m² = (100)² cm² = 10,000 cm². NOT 100 cm².
1 ft = 12 in. So 1 ft³ = 12³ in³ = 1,728 in³.

Word-problem unit traps:

Speed × time = distance — make sure all in matching units. 60 mph × 30 min doesn't equal 1,800 miles; convert minutes to hours first: $60 \cdot 0.5 = 30$ miles.
Density × volume = mass — units must match.

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Quick check

Try this SPR. Set up your conversion fractions so the unwanted units cancel. Multiply through; the leftover units should match the answer.

There are 5,280 feet in one mile. How many feet are in 5 miles?

Your answer:

Enter a whole number, fraction (e.g. 3/4), or decimal (e.g. .75).

Worked examples

Example 1

A bakery uses 24 cups of flour each day. How many gallons of flour does it use in 30 days, given that 16 cups = 1 gallon?

Example 2

A rectangular field measures 20 m by 30 m. What is its area in square feet, given that 1 m ≈ 3.28 ft?

Common pitfalls

Forgetting to square (or cube) the conversion factor for area / volume

$1 \text{ m} = 100 \text{ cm}$ doesn't mean $1 \text{ m}^2 = 100 \text{ cm}^2$ . It's $(100)^2 = 10{,}000 \text{ cm}^2$ . For volume: $(100)^3$ . Square the linear factor for square units; cube it for cubic units.

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Multiplying when you should divide (or vice versa)

Going from a bigger unit to a smaller unit (miles → feet), multiply. From smaller to bigger (feet → miles), divide. Or just write the fraction and cancel — let the units guide you.

Mixing units before converting

60 mph × 30 min doesn't directly give you a distance — the 60 is per hour, but you have minutes. Convert one to match: 30 min = 0.5 hr, so $60 \cdot 0.5 = 30$ miles.

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Reading the conversion factor wrong

1 mile = 5,280 feet means there are 5,280 feet IN 1 mile. To convert miles to feet, multiply by 5,280. To convert feet to miles, divide. Don't mix it up.

Key takeaways

Multiply by a conversion fraction equal to 1 (e.g., $\frac{60 \text{ min}}{1 \text{ hr}}$ ). Choose the orientation that cancels the unit you don't want.
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Chain fractions for multi-step conversions. Cancel as you go.
Square units need the conversion factor SQUARED. Cubic units cubed.
Always check that your units cancel correctly — the result should leave the desired unit.
Match all units before doing arithmetic in word problems (e.g., convert minutes to hours if speed is in mph).

Tracks your progress across lessons.

Checkpoint

10 questions on Ratios, Rates, Proportional Relationships, and Units, from our question bank. Score 70% or better across 10 answers to reach Silver and pass this step.

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Where this lesson fits

Before

Ratios and Proportions→

Unit Conversion

You are here

→Data Interpretation