Unit conversion is a pre-algebra topic that stops many students in their tracks. Questions about converting units pop up routinely on the SAT/ACT.
Basic conversions are easy to calculate by simple multiplication or division. More difficult problems require “Dimensional Analysis,” an easy and reliable way to perform conversion calculations.
The method is based on the following facts:
1. Equations relating units enable the creation of two fractions whose values are 1;
2. Multiplication by 1 never changes values and is therefore always allowed;
3. "Per" implies division.
To see how they enable the conversion of units using Dimensional Analysis, let's look at two questions.
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Simple example
1 mile = 5280 feet. Therefore, 1 mi / 5280 ft and 5280 ft / 1 mi are two fractions with values = 1. Let's convert 45 miles into feet. First write, as a fraction, the quantity to be converted: 45 miles / 1, and then multiply by 1 in the form of 5280 ft / 1 mi (we choose this fraction, with miles below, in order to cancel-out miles). Cancelling “mi” above and below leaves “ft” as the unit and 45 * 5280 as the calculation. So the answer is 237,600 ft.
Complex example
We'll convert 3500 meters per second squared to kilometers per hour squared. First write, as a fraction, the quantity to be converted: 3500 m/s^2. Since 1 kilometer = 1000 meters and 1 hour = 3600 seconds, multiply the initial fraction by 1 in the following forms: 1 km / 1000 m, 3600 s / 1 hr, and 3600 s / 1hr (to cancel s^2 below). Cancelling above and below leaves “m/ hr^2” as the unit and 3500 * 3600 * 3600 / 1000 as the calculation. So the answer is 45,360,000 km/hr^2.
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For practice, search Google for “converting units dimensional analysis worksheet,” pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this material.
To see how they enable the conversion of units using Dimensional Analysis, let's look at two questions.
-
Simple example
1 mile = 5280 feet. Therefore, 1 mi / 5280 ft and 5280 ft / 1 mi are two fractions with values = 1. Let's convert 45 miles into feet. First write, as a fraction, the quantity to be converted: 45 miles / 1, and then multiply by 1 in the form of 5280 ft / 1 mi (we choose this fraction, with miles below, in order to cancel-out miles). Cancelling “mi” above and below leaves “ft” as the unit and 45 * 5280 as the calculation. So the answer is 237,600 ft.
Complex example
We'll convert 3500 meters per second squared to kilometers per hour squared. First write, as a fraction, the quantity to be converted: 3500 m/s^2. Since 1 kilometer = 1000 meters and 1 hour = 3600 seconds, multiply the initial fraction by 1 in the following forms: 1 km / 1000 m, 3600 s / 1 hr, and 3600 s / 1hr (to cancel s^2 below). Cancelling above and below leaves “m/ hr^2” as the unit and 3500 * 3600 * 3600 / 1000 as the calculation. So the answer is 45,360,000 km/hr^2.
-
For practice, search Google for “converting units dimensional analysis worksheet,” pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this material.
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