Digital SAT · Math · Unit 3 · Problem Solving & Data

Lesson 3.2 · Unit Conversion

On the test: about 1 question a test — always solvable by writing the units down

Big idea. A conversion factor like 1 mile / 1609 m is a fraction equal to 1 (top and bottom are the same length). Multiplying by 1 never changes a quantity — it only changes its units. So write the factor the way up that makes the unwanted unit cancel, top against bottom.

🧑‍🏫 Rule 1 · Choose the factor that cancelsstep 1 of 5

1
📋 The question · SAT · March 2024 · Math 800 Book Q10
An ROV is at a depth of 41 fathoms. Depth in feet? (1 fathom = 6 feet)
(type the answer)
the question
$41 fathoms \to feet$
March 2024: 1 fathom = 6 feet.

🧑‍🏫 Rule 2 · A rate is a fraction of unitsstep 1 of 3

1
📋 The question · SAT · August US 2023 · Math 800 Book Q5
An object traveled 30 miles in 2 hours. Average speed in mph?
(type the answer)
speed
$\frac{30 mi}{2 h} = 15 \frac{mi}{h}$
August US 2023.

🎛 Move it · cancel the units

Flip each factor until only the units you want are left. A squared unit needs its factor TWICE.

6.80 \frac{m}{s \cdot s}

Tap a fraction to flip it. Each one equals 1, so flipping never changes the size — only which units cancel.

Units left: mi min^2⁻ ✓ = mi/min². Value ≈ 15.214

🧑‍🏫 Rule 3 · Squared units: use the factor twicestep 1 of 6

1
📋 The question · SAT · August US 2023 · Math 800 Book Q6
An object’s speed is increasing at a rate of 6.80 meters per second squared. What is this rate in miles per minute squared, rounded to the nearest tenth? (Use 1 mile = 1,609 meters.)
(type the answer)
the question
$6.80 \frac{m}{s ^{2}} \to \frac{mi}{min ^{2}}$
August US 2023.

Trap · the missing square

Using 3.28 only once for square feet is the classic trap — the wrong answer is always among the options.

🧑‍🏫 Rule 4 · Volume = mass ÷ densitystep 1 of 3

1
📋 The question · SAT · March US 2023 · Math 800 Book Q1
Two samples each have mass 3240 g. Sample A has density 3.0 g/cm³ and sample B 2.7 g/cm³. How much greater is B’s volume, in cm³?
(type the answer)
the question
$3240 g at 3.0 vs 2.7 \frac{g}{cm ^{3}}$
March US 2023: how much bigger is B’s volume?

🧑‍🏫 Rule 5 · Same units before multiplyingstep 1 of 3

1
📋 The question · SAT · November 2023 · Math 800 Book Q7
A garden box 3 ft by 27 ft is filled 24 inches high; the topsoil costs $198. Cost per cubic yard? (1 yd = 3 ft; 1 ft = 12 in)
(type the answer)
the question
$3 ft \times 27 ft \times 24 in$
November 2023: $198 of topsoil. Cost per cubic YARD?

Real question 1SAT · November 2024 · Math 800 Book Q14type the answer

An object’s speed is increasing at a rate of 5.70 meters per second squared. What is this rate in miles per minute squared, rounded to the nearest tenth? (Use 1 mile = 1,609 meters.)

🧑‍🏫 Rule · Cubic units: cube the factorstep 1 of 2

1
📋 The question · Gen Z Study
How many cubic feet are in 2 cubic yards? (1 yard = 3 feet)
(type the answer)
cube it
$1 yd^{3} = 3^{3} = 27 ft^{3}$
A cube 1 yard on a side is 3 × 3 × 3 cubic feet.

🧑‍🏫 Rule · amount = rate × timestep 1 of 2

1
📋 The question · Gen Z Study
A pump moves 15 gallons per minute. How many hours does it take to move 2,700 gallons?
(type the answer)
time
$2700 \div 15 = 180 min$

Take with you

▸Every conversion factor equals 1; write it so the unwanted unit cancels top-against-bottom.
▸A squared (cubed) unit needs its factor 2 (3) times.
▸Rates: keep units in the fraction — “gallons per square foot” is gallons ÷ ft².
▸Volume = mass ÷ density; convert every length to the target unit before multiplying.

Sign In to Keep Going