3. Unit Conversion and Measurement

Unit conversion means rewriting a measurement in different units without changing its value. The tool for this is dimensional analysis -- multiplying by a conversion factor written as a fraction equal to 1.

Dimensional analysis in three steps:

1. Write the original quantity as a fraction.
2. Multiply by a conversion fraction so the unwanted unit cancels.
3. Simplify.

Example: convert 72 miles per hour to feet per second.

• 72 miles/1 hr x 5,280 ft/1 mile x 1 hr/3,600 sec
• The 'miles' cancel and the 'hr' cancel: 72 x 5,280 / 3,600 = 105.6 ft/sec.

Common SAT® conversion facts you should know:

• Length: 1 foot = 12 inches; 1 yard = 3 feet; 1 mile = 5,280 feet.
• Time: 1 minute = 60 seconds; 1 hour = 60 minutes.
• Weight: 1 pound = 16 ounces; 1 ton = 2,000 pounds.
• The SAT® provides metric conversions in the reference sheet when needed.

Reading conversion tables: The Digital SAT® sometimes gives a table of conversion factors or exchange rates and asks you to convert a given quantity. Identify which row or column matches the units you are starting with, then multiply or divide as indicated.

Worked example: A recipe calls for 3.5 cups of milk. A chef has a container that holds 2 pints. 1 pint = 2 cups. Does the chef have enough?

• Convert pints to cups: 2 pints x 2 cups/pint = 4 cups.
• 4 cups > 3.5 cups, so yes, the chef has enough.

• Multi-step conversions: chain the fractions so each unwanted unit cancels before you multiply everything out.
• Rate conversions: when converting rates (like mph to m/s), convert both the numerator and denominator units separately.

⚠️ Common mistake: multiplying when you should divide (or vice versa) during unit conversion. If the answer seems unreasonably large or small, you probably used the conversion factor upside-down.

💡 Tip: write the units in your conversion fraction so they visually cancel like variables in algebra. If the unwanted unit does not cancel, flip the fraction.