Chapter 5—Powers, Exponents, and Roots
5-7 Working with Engineering Notataion
When you complete the work for this section, you should be able to: - Describe how the power-of-10 exponents for engineering notation must be multiples of 3.
- Rewrite the coefficient of any power-of-10 expression so that the exponent is a multiple of 3.
- Name all of the prefixes for engineering notation, from nano- to Giga-.
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Introduction to Engineering Notation
| Definition  Engineering notation is a special form of power-of-10 notation where the exponents for the 10s must be 0 or multiples of 3. There must be 1, 2, or 3 digits on the left side of the decimal point. |
| Examples Examples of valid powers of 10 for engineering notation are: 103 106 109 10 –3 10 –6 10 –9 100 Examples of invalid powers of 10 for engineering notation are: 102 104 105 107 10 –2 10 –4 10 –1 | | Notes Valid powers-of-10 for engineering notation must be multiples of 3. Notice that 0 (zero) is also a valid power of 10 for scientific notation. Recall that 100 = 1 Because the exponent for the base-10 must be 0 or a multiple of 3, the coefficient cannot always be a value between -9 and 9. Instead, the coefficients for engineering notation will be between -999 and 999. | |
Examples and Exercises
Identify Valid Scientific Notation Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
Rewriting Decimals and Power-of-10 Values in Engineering Notation
A common procedure in career mathematics is to adjust decimal values to conform to the standards of engineering notation.
Example
Consider this value expressed in a simple power-of-10 notation: 23.45 x 104.
- First, look at the exponent, 4. It should be changed to something such as 3 or 6. Let's try 3.
- Recall that when you decrease an exponent, you must move the decimal point to the right. So in this example: 23.45 x 104 becomes 234.5 x 103
- ... and 234.5 x 103 is a valid expression in engineering notation — there are between one and three digits on the left side of the decimal point in the coefficient, and the exponent is a multiple of three.
But what about changing the exponent in 23.45 x 104 from 4 to 6, instead of from 4 to 3. Watch what happens:
Increasing the exponent by 2 means you must move the decimal point in the coefficient two places to the left. So 23.45 x 104 becomes .2345 x 106.
... but this is not really a valid expression of engineering notation. The exponent is, indeed, a multiple of 3, but there are no digits (remember, 0 doesn't count) on the left side of the decimal point in the coefficient.
- 23.45 x 104 is not expressed in proper engineering notation
- 0.2345 x 106 does not express the the value in proper engineering notation.
- 234.5 x 103 is a proper expression of scientific notation.
More Examples
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Use this scroll bar to view all of the examples. |
| Remember - When you move the decimal point in the coefficient to the right, you must also decrease the power-of-10 exponent by the same number of units.
- When you move the decimal point in the coefficient to the left, you must also increase the power-of-10 exponent by the same number of units.
- When you increase the value of the power-of-10 exponent, you must also move the decimal point the same number of units to the left.
- When you decrease the value of the power-of-10 exponent, you must also move the decimal point the same number of units to the right.
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Examples and Exercises
Rewriting Values with Engineering Notation Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
