Adding and Subtracting 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 not the same then it is necessary to change one of the numbers so that both numbers have the same exponential value.

Part 1 Adding in Scientific Notation

Adding… The general format for adding is as follows… (N x 10x) + (M x 10x) = (N + M) x 10x The first step, if necessary, is to change one of the numbers so that both numbers have the same exponential value.

Adding… Secondly, add the N and M numbers together and express as an answer. The final step is to multiply the result by the 10x. (It may be necessary to put the resulting answer into proper scientific notation.)

Adding With the Same Exponent (3.45 x 103) + (6.11 x 103) 3.45 + 6.11 = 9.56 9.56 x 103

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 If you had adjusted the exponents originally to the 6th power, you would end up with the same result

Now it’s your turn. (6.89 x 104) + (9.24 x 105)

Part 2 Subtracting in Scientific Notation

Subtracting… The general form for subtracting is as follows… (N x 10x) – (M x 10x) = (N – M) x 10x The first step, if necessary is to change one of the numbers so that both numbers have the same exponential value. (Just like adding).

Subtracting… Secondly, subtract the M number from the N number and express as an answer. The final step is to multiply the result by the 10x. (It may be necessary to put the resulting answer into proper scientific notation.)

Subtracting With the Same Exponent (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) (4.23 x 103) – (0.956 x 103) 4.23 – 0.956 = 3.274 3.274 x 103 If you had adjusted the exponents originally to the 2nd power, you would end up with the same result.

Now it’s your turn. (7.83 x 108) - (2.5 x 106)

Extended Examples (7.45 x 108) - 11,610,000