Concept 5

Apply unit conversion and derived units (dimensional analysis).

Core Idea

Multiply by conversion factors written as fractions equal to 1. Arrange them so unwanted units cancel and desired units remain.

Understanding

Rule: conversion factors are forms of 1, so they change units without changing value.

  1. Start with the quantity you know.
  2. Multiply by fractions that place the unwanted unit opposite its match so it cancels.
  3. Keep chaining until only the desired unit remains.

Example: 15 fts ×1 mi5,280 ft ×3,600 s1 hr ≈10.23 mihr.

The SAT gives you the conversion factors you need. The main job is setting them up so the units cancel in the right order.

Step by Step

  1. Write the starting quantity with its units.
  2. Identify which units need to change.
  3. Write conversion factors as fractions so unwanted units will cancel.
  4. Multiply across. Cancel units first, then compute the number.

Misconceptions

  • Flipping a conversion factor — putting the wrong unit in the numerator, so units multiply instead of canceling.
  • Forgetting to convert both parts of a compound unit (e.g., converting feet to miles but leaving seconds as seconds).
  • Squaring or cubing the conversion factor when converting area or volume units — 1𝑓𝑡2 =144𝑖𝑛2, not 12𝑖𝑛2.
Question

Worked Example

A factory produces 480 parts per hour. Each part has a mass of 250 grams. What is the total mass, in kilograms, of parts produced in 6 hours?

Select an answer to see the explanation