Chapter 5—Powers, Exponents, and Roots
5-6 Engineering Notation
| When you complete the work for this section, you should be able to: |
Multiplying and Dividing Powers of Ten
Procedure  To multiply powers of 10: - Multiply the coefficients of the factors. The result is the coefficient of the product.
- Add the exponents of the factors. The result is the exponent of the product.
Of course the base of 10 remains unchanged. |
Examples of Mulitiplying Powers of Ten
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Use this scroll bar to view all of the examples. |
Examples and Exercises
Multiplying Powers of Ten Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
Procedure  To divide powers of 10: - Divide the coefficients of the terms — numerator divided by denominator. The result is the coefficient of the quotient.
- Subtract the exponents of the terms — numerator minus denominator. The result is the exponent of the quotient.
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Example
Problem | ( 9 x 108 ) | = _____ | | ( 3 x 102 ) | | |
| Procedure | |
- Divide the coefficients.
| 9 / 3 = 3 |
- Subtract the exponents.
| | ( 9 x 108 ) | = _____ | | ( 3 x 102 ) | 8 – 2 = 6 |
- Assemble the results
| 3 x 106 |
Solution | ( 9 x 108 ) | = 3 x 106 | | ( 3 x 102 ) | | |
Example
Problem | ( 3.6 x 108 ) | = _____ | | ( 2 x 10 -4 ) | | |
| Procedure | |
- Divide the coefficients.
| | ( 3.6 x 108 ) | | ( 2 x 10 -4 ) | 3.6 / 2 = 1.8 |
- Subtract the exponents.
| | ( 3.6 x 108 ) | | ( 2 x 10 -4 ) | 8 – ( –4 ) = 12 |
- Assemble the results
| 1.8 x 1012 |
Solution | ( 3.6 x 108 ) | = 1.8 x 1012 | | ( 2 x 10 -4 ) | | |
Examples and Exercises
Dividing Powers of Ten Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
Procedures Review To multiply powers of ten: - Multiply the coefficients
- Add the exponents
To divide powers of ten: - Divide the coefficients
- Subtract the exponents
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Adding and Subtracting Powers of Ten
| Adding and subtracting powers of ten can be a bit more complicated than multiplying and dividing. The main problem is that powers of ten can be added or subtracted only when both terms have the same exponent. In other words, it is okay to add or subtract 2.1 x 102 and 1.4 x 102 because they both have the same exponent. But consider 6.8 x103 and 3.4 x 104. Those terms cannot be added or subtracted in their given form–one has to be rewritten so that its exponent is equal to the exponent of the other term. | Important Powers of ten can be added or subtracted only when their exponents are equal. | |
Procedures  To add powers of ten:
- Make sure the terms have the same power of ten.
- Add the coefficients
- Assign the common power of ten
To subtract powers of ten: - Make sure the terms have the same power of ten.
- Subtract the coefficients
- Assign the common power of ten
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It is easy to add and subtract powers of ten when the exponents are already identical.
Examples
| 1. 3 x 104 + 5 x 104 = 8 x 104 | 2. 8.2 x 108 – 1.1 x 108 = 7.2 x 108 | 3. 2 x 10-3 + 4 x 10-3 = 6 x 10-3 |
Examples and Exercises
Introduction to Adding and Subtracting Powers of Ten Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
When the exponents are not the same, you must rewrite one of the terms so that the exponents are equal. It really makes no difference which terms you change—just so the exponents end up being equal. After that, simply add or subtract as in the previous examples in this lesson.
Example
Problem 4 x 103 + 2 x 102 = _____ | |
| Procedure | |
- Rewrite one of the terms so that the exponents are equal.
| 4 x 103 = 40 x 102 |
- Complete the addition
| 40 x 102 + 2 x 102 = 42 x 102 |
Solution 4 x 103 + 2 x 102 = 42 x 102 or 4.2 x 103 | |
Example
Problem 12 x 108 – 5 x 1010 = _____ | |
| Procedure | |
- Rewrite one of the terms so that the exponents are equal.
| 5 x 1010 = 500 x 108 |
- Complete the addition
| 12 x 108 – 500 x 108 = – 488 x 108 |
Solution 12 x 108 – 5 x 1010 = – 488 x 108
or – 4.88 x 1010 | |
Examples and Exercises
Adding and Subtracting Powers of Ten Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
