SAT Math formula sheet · all 24 · Problem-Solving and Data Analysis · #13 of 24

Unit conversions on the SAT: How It Is Tested

Ratios, rates, proportional relationships, and units

Unit Conversions diagram for the SAT: Per makes the fraction. Line the units up so each one cancels: whatever is on the bottom of one fraction goes on top of
What it is really testingPer makes the fraction. Line the units up so each one cancels: whatever is on the bottom of one fraction goes on top of the next. If a unit is squared, square the whole conversion factor, or the units will not cancel.

The question from the sheet

Hard
SAT Problem-Solving and Data Analysisanswer B
The speed of a sled is increasing at a rate of 8.68.6 meters per second squared. What is this rate, in miles per minute squared, rounded to the nearest tenth? (Use 11 mile =1,609= 1{,}609 meters.)
A230.6230.6
✓19.219.2
C0.30.3
D3.83.8

How the diagram applies

  1. Chain the fractions so each unwanted unit cancels: 8.6 ms2×1 mi1,609 m×(60 s1 min)2\dfrac{8.6\ \text{m}}{\text{s}^{2}} \times \dfrac{1\ \text{mi}}{1{,}609\ \text{m}} \times \left(\dfrac{60\ \text{s}}{1\ \text{min}}\right)^{2}
  2. Seconds are squared, so the seconds-to-minutes factor is applied twice: 602=3,60060^{2} = 3{,}600.
  3. 8.6×3,6001,609≈19.2\dfrac{8.6 \times 3{,}600}{1{,}609} \approx 19.2 miles per minute squared.

Answer: B

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Common Questions

It comes up as an SAT ratios, rates, proportional relationships, and units question. Per makes the fraction. Line the units up so each one cancels: whatever is on the bottom of one fraction goes on top of the next. If a unit is squared, square the whole conversion factor, or the units will not cancel.

Chain the fractions so each unwanted unit cancels: 8.6\ ms^2 × 1\ mi1,609\ m × (60\ s1\ min)^2 Seconds are squared, so the seconds-to-minutes factor is applied twice: 60^2 = 3,600. 8.6 × 3,6001,609 19.2 miles per minute squared.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Unit Conversions is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.