Adding and Subtracting Numbers in Scientific Notation

Adding/Subtracting when Exponents are Equal When the exponents are the same for all the numbers you are working with, add/subtract the base numbers then simply put the given exponent on the 10.

General Formulas (N X 10x) + (M X 10x) = (N + M) X 10x (N X 10y) - (M X 10y) = (N-M) X 10y

Example 1 Given: 2.56 X 103 + 6.964 X 103 Add Base Numbers: Answer: 9.524 X 103

Example 2 Given: 9.49 X 105 – 4.863 X 105 Subtract Base Numbers: Answer: 4.627 X 105

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

Subtracting With the Same Exponent (8.96 x 107) – (3.41 x 107) (8.96 – 3.41) x 107 5.55 x 107

Adding/Subtracting when the Exponents are Different

When adding or subtracting numbers in scientific notation, the exponents must be the same. If they are different, you must move the decimal either right or left so that they will have the same exponent.

Moving the Decimal For each move of the decimal to the right you have to subtract 1 from the exponent. For each move of the decimal to the left you have to add 1 to the exponent.

Moving the Decimal Or…. If you make the exponent bigger, you must make the base number smaller. If you make the exponent smaller, you must make the base number bigger

Continued… It does not matter which number you decide to move the decimal on, but remember that in the end both numbers have to have the same exponent on the 10.

Example 1 Given: 2.46 X 106 + 3.476 X 103 Shift decimal 3 places to the left for 103. New number is: 0.003476 X 103+3 Add: (2.46 + 0.003476) X 106 Answer: 2.463 X 106

Example 2 Given: 5.762 X 103 – 2.65 X 10-1 Shift decimal 4 places to the right for 10-1. New number is: 0.000265 X 10(-1+4) Subtract: (5.762 -.000265) X 103 Answer: 5.762 X 103

Example 3 (4.12 x 106) + (3.94 x 104) (412 x 104) + (3.94 x 104) Express in proper form: 4.15 x 106