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Mathematics for Technology I (Math 1131)

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Durham College, Mathematics
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Converting Units using Conversion Factor

Any quantity that is measurable needs a unit to describe how large or small it is relative to another quantity. For example, 1 meter is a unit of length, 1 second is a unit of time, and 1 m/s (one meter per second) is a unit rate.

To convert from one unit to another, a conversion factor (also known as conversion ratio) is required; a conversion factor is used to express a quantity in different units of measurement. For example, to convert from 150 seconds to minutes, you use the known conversion factor 60 seconds = 1 minute. For more complicated unit conversions, conversion factors are provided by your teacher.

The video below demonstrates how to use a known conversion factor to go from one unit to another. You’ll notice that in example (3), sometimes a conversion factor may not be given. For example, you may be given:

2.54 cm = 1 in

But the question may ask you to go from cm² to inches². In this case, you will have to modify your conversion factor to look the way you want it to look.


Oftentimes you may need to convert from metric units to imperial units. The basic metric units are meters (for length), grams (for mass or weight), and liters (for volume), while their equivalents imperial counterparts are inches, feet, and miles (for length), pounds (for mass or weight), and gallons (for volume), respectively. Unlike the imperial system, the metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement mentioned above – meter, liter, or gram. Luckily, to go from metric to imperial, all that’s needed is a conversion factor, so the process doesn’t change.

Let’s watch a few examples of this in action:

As mentioned above, the base unit of measurement in the metric system can be modified by adding prefixes to unit. Each prefix has a specific meaning when applied to the base unit that indicates multiples or fractions of the units. In other words, the prefixes of the metric system, such as kilo- and milli-, represent multiplication by powers of ten. Once again, if you know how to convert units, converting from one prefix to another is just as simple. Here are a few examples of this in action:

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