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Chapter 5—Powers, Exponents, and Roots 55 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:  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 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:  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.
 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:  Multiply the coefficients
 Add the exponents
 To divide powers of ten:  Divide the coefficients
 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 10^{2} and 1.4 x 10^{2} because they both have the same exponent. But consider 6.8 x10^{3} and 3.4 x 10^{4}. 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
 It is easy to add and subtract powers of ten when the exponents are already identical. Examples 1. 3 x 10^{4} + 5 x 10^{4} = 8 x 10^{4}  2. 8.2 x 10^{8} – 1.1 x 10^{8} = 7.1 x 10^{8}  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
