Due to the hard work of others many years ago, there are now rigorous systems for describing most physical quantities that we regularly encounter: lengths, weights, time and more. However, what happens when information is presented in different units? Unit conversion is necessary to examine quantities on equal footing.

## How to Convert 1 Meter to Inches and Feet

Meters, inches and feet are all units of length. Meters are the standard unit of length in the metric system, and inches and feet are standard units of length in the Imperial system. You can use conversion factors to convert a quantity described in one unit to another.

One meter is equal to 3.28 feet, and 1 foot is equal to 12 inches. Therefore, 1 meter is equal to 3.28 × 12 inches, or 39.36 inches. The meter-to-inches formula is therefore simple: Multiply the number of meters that need to be converted by 39.37 inches, to get the resulting length in inches.

With this information, it is possible to complete many length conversions from the metric system to Imperial units.

## The General Concept of Unit Conversion

In order to convert one unit to another, we need to be able to transform the quantity into another unit, without changing the quantity represented. Therefore, the most important part of unit conversion is knowing the conversion factor between two units. For example, there are 12 inches in 1 foot, and 100 centimeters in 1 meter; therefore, 12 inches = 1 foot and 100 cm = 1 m are accurate equations.

The reason knowing the conversion factor is the most important is because it is a form of the number 1, and multiplying a number by 1 does not change the quantity. In the case of conversion, the conversion factor is the multiplicative factor that equals 1.

## Examples of Length Conversion

We have already covered the meter-to-feet conversion: 1 meter equals 3.28 feet. Using the previous formula, one can now use the conversion factor to quickly convert meters to feet.

However, quite often quantities in the metric system are described by prefixes that signify the order of magnitude of the number: millimeters, microseconds, picograms and so on. The standard in each of the previous examples is meters, seconds and grams respectively, and the prefix allows us to specify the order of magnitude more quickly.

For example, the diameter of a human hair can range from 0.000017 meters, to 0.000181 meters. We can rewrite this using powers of 1o. In this case, we need about 6 factors of 10^{-1}, or 10^{-6}, which is called a micrometer or micron. Therefore the diameter of human hair can range from about 17 microns to 181 microns.

But what is that range in inches? We know the conversion from meters to inches, which means we know how to convert micrometers to inches as well. If 1 meter equals 39.36 inches, then 1 micrometer is simple: 10^{-6} times 39.36 inches. Therefore the diameter of human hair can range from about 0.00067 inches to 0.0071 inches.

The prefix system does not work in imperial units, in which case small quantities are often rewritten in scientific notation, for ease of use.

References

Tips

- Double-check your math.

Warnings

- Do not round your answer to any other decimal places than what the problem requires. If you need your answer to 4 decimal places, round the initial numbers to 4 decimal places. Otherwise, your answer will be inaccurate.

About the Author

Lipi Gupta is currently pursuing her Ph. D. in physics at the University of Chicago. She earned her Bachelor of Arts in physics with a minor in mathematics at Cornell University in 2015, where she was a tutor for engineering students, and was a resident advisor in a first-year dorm for three years. With this experience, when not working on her Ph. D. research, Gupta participates in STEM outreach activities to promote young women and minorities to pursue science careers.