Adding and Subtracting Numbers in Scientific Notation A.Oman Ellerbruch.nmu.edu

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

Example 1 Given: 2.56 X X 10 3 Add: = Answer: X 10 3

Example 2 Given: 9.49 X 10 5 – X 10 5 Subtract: 9.49 – = Answer: X 10 5

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 add -1 to the exponent. For each move of the decimal to the left you have to add +1 to the exponent.

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 X 10 3 Shift decimal 3 places to the left for Move: X Add: 2.46 X X 10 6 Answer: X 10 6

Example 2 Given: X 10 3 – 2.65 X Shift decimal 4 places to the right for Move: X 10 (-1+4) Subtract: X X 10 3 Answer: X 10 3

Practice Worksheet Practice Adding and Subtracting in Scientific NotationPractice Adding and Subtracting in Scientific Notation Answers to Worksheet

Links for more information and practice Addition and Subtraction with Scientific NotationAddition and Subtraction with Scientific Notation Problem Solving--Scientific Notation Scientific Notation