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How to Convert 20 cm to inches

Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

How many inches does 20 centimeters represent? This lesson goes over how to convert from metric units of distance to standard units of distance in a step-by-step fashion.

Steps to Solving the Problem

Converting units can be tricky. Let' say you are measuring with a ruler that is marked in centimeters. You get a measurement of 20 cm, but you need to know what that is in inches. How could you do that?

Converting from one set of units to another involves multiplying by a conversion factor. A conversion factor is composed of both numbers and units in a fraction. The units on the top and bottom of this fraction represent the same measurement but are expressed in different units.

  • Step 1 - Use the correct conversion factor

1 inch (in) is the same length as 2.54 centimeters (cm). So, what is the conversion factor to go from centimeters to inches?

To get this conversion factor we put the units we are converting to on the top, and the units we are converting from on the bottom, like this:

(1 in) / (2.54 cm)

  • Step 2 - Multiply by the number of old units we have

Our original problem was converting 20 centimeters to inches, so we'll multiply by 20 cm:

{(1 in) / (2.54 cm)} (20 cm)

This step actually has 2 parts:

  • Step 2, part 1 - Check units

At this point, it's important to check and make sure the units will come out correctly. In this case, we have units of centimeters on both the top and bottom of the fraction. Since a centimeter divided by a centimeter is just equal to 1 with no units, we say the units cancel out. This leaves us with units of inches, which is the unit we were hoping to have for our final answer. Now we can go on to part 2

  • Step 2, part 2 - Perform calculations

Since we have checked the units, we can ignore them for now and just look at the math.

(1 / 2.54)(20) = (1 x 20) / 2.54 = 20 / 2.54 = 7.87

Solution

To get the solution, we put the two parts of Step 2 together to form our answer: 7.87 inches.

Checking Your Work

There are a number of ways to check your work on problems involving conversion factors:

  • 'Does my answer make sense?'

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