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Converting lengths is a necessary skill in physics. If you’ve grown up in the metric system, meters come naturally.  Unfortunately in the United States, most of us think in terms of inches, feet, and miles. Let’s take some time to learn to convert between metric and imperial units at these scales.

## Inches to Centimeters

Even though it evolved long before the metric system, the imperial system these days is defined by the metric system. The first conversion factor you should memorize is the conversion that defines the inch in terms of centimeters. One inch equals 2.54 centimeters.

This is an exact definition, meaning that you should always use 2.54 for the conversion.  Even though you could estimate things using 2.5, try to memorize the 2.54 cm number.

If an object, say a pen is 6 inches long, you can find its length in cm by multiplying by 2.54 cm/in.  If you know the length of an object in cm, you can determine its length in inches by dividing by 2.54 cm/in.

I’ve always had trouble remembering whether I should multiply or divide. Here’s a better way than just guessing or trying to remember:  Think of the conversion as a fraction.

1.00 in = 2.54 cm becomes

Remember that you can multiply any number by 1 and not change its value.  Therefore we can set up an equation to convert, and simply multiply by the version that allows us to cancel out the unwanted

## Example of Converting Lengths

Let’s try to convert 6.00 inches into centimeters.

We start out by simply writing down that 6.00 inches equals 6.00 inches times 1.

This seems a bit like overkill, but it will help us avoid making silly looking mistakes.

We next replace the 1 with the version of the conversion equation that puts the inches on the bottom so that it will cancel out the inches we started with.

Now we do the math, multiplying 6.00 times 2.54 and dividing by 1 to get 15.24.  This is followed by the units, inches times centimeters divided by inches.

As our last step, we look at the units and see that the inches in the numerator can cancel out the inches in the denominator, leaving us with

This is our final answer, 6.00 inches equals 15.24 centimeters.

Notice that we have one more number in our centimeter number. If we were following strict rules about significant digits, this would be reported as 6.00 in = 15.2 cm.  We will talk about the rules of significant digits later.  For now, keep the number of digits you display about the same as you started with.