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Chapter 5—Powers, Exponents, and Roots

5-5 Working with Powers of Ten

This is where you learn about:

  • Multiplying and Dividing Powers of Ten
  • Adding and Subtracting Powers of Ten

Multiplying and Dividing Powers of Ten

Procedure

To multiply powers of 10:

  1. Multiply the coefficients of the factors. The result is the coefficient of the product.
  2. Add the exponents of the factors. The result is the exponent of the product.

Of course the base of 10 remains unchanged.

Examples of Multiplying Powers of Ten

Examples & Exercises

Multiplying Powers of Ten

Use these interactive Examples & Exercises to strengthen your understanding and build your skills:

 

Procedure

To divide powers of 10:

  1. Divide the coefficients of the terms — numerator divided by denominator. The result is the coefficient of the quotient.
  1. Subtract the exponents of the terms — numerator minus denominator. The result is the exponent of the quotient.

Examples of Dividing Powers of Ten

Examples & Exercises

Dividing Powers of Ten

Use these interactive Examples & Exercises to strengthen your understanding and build your skills:

 

Procedures Review

To multiply powers of ten:

  1. Multiply the coefficients
  2. Add the exponents

To divide powers of ten:

  1. Divide the coefficients
  2. Subtract the exponents

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:

  1. Make sure the terms have the same power of ten.
  2. Add the coefficients
  3. Assign the common power of ten

To subtract powers of ten:

  1. Make sure the terms have the same power of ten.
  2. Subtract the coefficients
  3. Assign the common power of ten

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 = 7.1 x 108 3.   2 x 10-3 + 4 x 10-3 = 6 x 10-3

When the exponents are not the same, you must rewrite one of the terms so that they are. It really makes no difference which terms you change—just so the exponents end up being equal. After that, simply add or subtract the coefficients and attach the common power of ten.

Note

It makes no difference which terms you change in order to match the values of their exponents. The results will look different, but they will be equal.

Examples of Adding and Subtracting Powers of Ten

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