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GED Math: Tutoring Solution29 chapters | 304 lessons

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Lesson Transcript

Instructor:
*Gerald Lemay*

Gerald has taught engineering, math and science and has a doctorate in electrical engineering.

Both meters per second and miles per hour are valid units for speed and velocity. In this lesson, you will learn a quick way to convert from one unit to the other. We'll also see how we can make this conversion more accurate.

To convert a speed in meters per second to a number of miles per hour, we use:

- 1 meter per second = 2.2369 miles per hour, accurate to 5 significant figures

Let's do an example to outline the steps used in the conversion:

The average walking speed of an adult is 1.34 meters per second. What is this speed in miles per hour?

Multiply the given value with the conversion factor. We know the conversion factor is 2.2369. Therefore:

- 1.34(2.2369) = 2.997446

Determine the number of significant figures:

- The number 1.34 has 3 significant figures
- The number 2.2369 has 5 significant figures

Round the answer to the lesser number of significant figures. Since the lesser number of significant figures is 3, we round the answer to 3 significant figures:

- 2.997446 rounds to 3.00 when we keep 3 significant figures

Thus, 1.34 meters per second converts to 3.00 miles per hour.

Another way to say how to convert *x* meters per second to miles per hour is to multiply *x* by 2.2369 and then round to the number of significant figures in *x*. This solution will work for most of the cases you encounter. Of course, if *x* has more than 5 significant figures, we will need a more accurate conversion factor.

The conversion factor, 2.2369, has 5 significant figures and works very well when the speed to be converted is a number of meters per second with 5 or less significant figures. We will now show where the number, 2.2369, comes from and how to extend it to have more significant figures.

Speed is a measure of distance and time. We can develop our ability to do unit conversions, by looking at time and distance separately.

First, time. There are 3600 seconds in 1 hour:

Second, distance. The following conversion factors are completely accurate:

- 5280.00 feet = 1.00 mile
- 12.00â€¦ inches = 1.00 foot
- 2.5400â€¦ cm = 1.00 inch
- 100.00â€¦ cm = 1.00 m
- 1000.00â€¦ m = 1.00 km

Combining these conversion factors so the units cancel:

Everything except miles over hours cancels out:

The result is 2.236936292054402â€¦ and is only limited in accuracy by the word size of the computer or calculator. The idea is to round this conversion factor to a number of significant digits which is at least one more than the accuracy of the number to convert.

For example, let's convert 9.10575 meters per second to miles per hour.

Select the accuracy for the conversion factor. The number 9.10575 has 6 significant figures. Thus, round the conversion factor, 2.236936292054402â€¦, to 7 significant figures, which is:

- 2.236936

Multiply by the conversion factor. The conversion factor is 2.236936, so:

- 9.10575(2.236936) = 20.36897998200

Determine the number of significant figures.

- The number 9.10575 has 6 significant figures
- The number 2.236936 has 7 significant figures

Round the answer to the lesser number of significant figures. The lesser number of significant figures is 6 so we round the answer to 6 significant figures, which is:

- 20.36897998200â€¦ rounds to 20.3690

Thus, 9.10575 meters per second converts to 20.3690 miles per hour.

We have discovered how to convert meters per second to miles per hour. Now that you understand the basics of 1 meter per second = 2.2369 miles per hour and being accurate to 5 significant figures, you can use this equation any time you need it!

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16 in chapter 7 of the course:

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GED Math: Tutoring Solution29 chapters | 304 lessons

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