Adding and Subtracting Coefficients, Bases and Powers, Oh My! By: Jenny Erickson Modified by Vicki Ibarra

Adding in Scientific Notation and Subtracting in Scientific Notation

Adding and Subtracting… The important thing to remember about adding or subtracting is that the exponents must be the same! If the exponents are the same then it is fine to “factor” out the base of 10 and exponent. Then just work with the coefficients (the numbers in the front)

EXAMPLE 1 Adding With the Same Exponent (3.45 x 103) + (6.11 x 103) 3.45 + 6.11 = 9.56 Factor out the 103 (just pretend it is not there) Combine coefficients and put the 103 back on the end 9.56 x 103 Try it in your calculator

Adding… with different exponents The first step, if necessary, is to change one of the coefficients so that both numbers have the same exponential value. This is fairly simple after you get the hang of it 6.2 x103 + 2.14 x 102 6.2 x103 = 6200 and so does 62 x 102 62 + 2.14 = 64.14 don’t forget the 102 64.14 x 102 Remember to express in proper form 6.414 x103

Adding With Different Exponents (4.12 x 106) + (3.94 x 104) (412 x 104) + (3.94 x 104) 412 + 3.94 = 415.94 415.94 x 104 Express in proper form: 4.15 x 106

Subtracting… Both coefficients must have the same exponential value. (Just like adding). (It may be necessary to put the resulting answer into proper scientific notation.)

Subtracting With the Same Exponent Remember, same rules as adding. (8.96 x 107) – (3.41 x 107) 8.96 – 3.41 = 5.55 5.55 x 107

Subtracting With Different Exponents (4.23 x 103) – (9.56 x 102) (42.3 x 102) – (9.56 x 102) 42.3 – 9.56 = 32.74 32.74 x 102 Express in proper form: 3.27 x 103