Unit Conversion and Dimensional Analysis

SAT Math · Axiom Academy

Unit Conversion & Dimensional Analysis Master conversion factors and multi-step unit conversions Understanding Conversion Factors A conversion factor is a ratio equal to 1 that expresses how many of one unit equal another unit. You can multiply by conversion factors without changing the actual value. Example 1: Simple Unit Conversion Notice: we use the conversion factor with feet in the denominator so the feet unit cancels. Dimensional analysis is the systematic method of converting between units by canceling units. The key is to set up conversion factors so that unwanted units cancel and desired units remain. Example 2: Multi-Step Conversion Example 3: Complex Multi-Step Conversion Convert 60 miles per hour to feet per second. Converting rates (like miles per hour) requires converting both the numerator and denominator, often using multiple conversion factors. A printer prints 15 pages per minute. How many pages per hour? Example 5: Density Conversions Convert 2 grams per cubic centimeter to kilograms per liter. (Note: 1 liter = 1000 cubic centimeters) Keep units visible: Write units throughout—they guide you to the correct setup Cancel carefully: Make sure the unit you want to cancel is in the numerator of the conversion factor Check reasonableness: If converting to smaller units, you should get a bigger number (and vice versa) Compound conversions: For complex problems, break into simple steps Memorize key factors: Knowing common conversions helps you work faster

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