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How Unit Conversions Work and How to Do Them

A step-by-step explanation/tutorial on how to use conversion factors.

How to Convert Units

Converting units means using different terms of measurements, but not changing the thing that is actually measured - length, mass, etc.

For example, on the ruler shown below, there are markings for both inches and centimeters. They both measure length, but in different units.

ruler

But if your ruler only has inch markings, and you need to know the length of something in centimeters, then you are going to have to convert units.

The trick for doing this is to have a special way of multiplying by 1, so that the number changes, and the units change, but the thing being measured does not change.

The 'special way of multiplying by one' is to use the correct conversion factor.

Here's an example: we want to convert feet to meters - say we have a piece of wood 2 feet long, we want to know how many meters that is.

Equation 1

2 feet X (conversion factor) = ? meters

The conversion factor will be a ratio or fraction. It will have the unit we want - meters, in this case - in the numerator (top) and the unit we have - feet - in the denominator (bottom).

Equation 2

2 feet X ? meters
? feet
= ? meters

This is so that the old units will 'cancel out', leaving us with the new units.

Equation 3

2 feet X ? meters
? feet
= ? meters

Now we need to assign numbers to the question marks in the conversion factor. This is easy in the denominator, we will just set it equal to 1. This way the numerator becomes the 'real' conversion factor.

Equation 4

2 feet X ? meters
? feet
= ? meters

You can't 'figure out' the conversion factor in the numerator - you have to look it up, or at least determine it with information outside the problem. It's determined by the ratio between the two different measurement systems.

I looked it up for you. The feet-to-meters conversion factor is 0.3048. See where conversion factors come from, below, for more info about this.

Equation 5

2 feet X 0.3048 meters
1 foot
= ? meters

Notice - this is a key point - that 0.3048 meters equals 1 foot. Because of this, the conversion factor is the 'special way of multiplying by 1' that we mentioned earlier.

0.3048 meters = 1 foot So 0.3048 meters
1 foot
= 1

Now do the math.

Equation 6

2 feet X 0.3048 meters
1 foot
= 0.6096 meters

Where Conversion Factors Come From

This is a very short version of a long story. See Wikipedia: Measurement for a longer version. Also see Wikipedia: Conversion of Units for a long list of conversion factors.

Today the metric system, as specified by the International System of Units, is accepted as the standard. In this system various units, such as meters, liters, grams, etc. are defined in terms of various physical phenomena. For example, the meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.

'English' units, like feet, gallons, and pounds, are defined only in terms of the metric system. In other words, there is no definition of how long an inch is, except in terms of the metric system. As it happens, one inch is defined as exactly 2.54 centimeters.

So, where did we get the 0.3048 meters = 1 ft conversion factor? We built it from some other factors we knew.

1 foot X 12 inches
1 foot
X 2.54 cm
1 inch
X 1 meter
100 cm
= 0.3048 meters

Each of the conversion factors we used is, as above, a 'special way of multiplying by 1'.

Conversion Calculator

This covers the conversions shown in Visual Metric Conversion Charts.

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