Adding and Subtracting Numbers in Scientific Notation January 2, 2014

When adding or subtracting numbers in scientific notation, the exponents must be the same.

Adding/Subtracting when Exponents are THE SAME Step 1 - add/subtract the decimal Step 2 – Bring down the given exponent on the 10

Step 2 – Bring down exponent : Example 1 (2.56 X 103) + (6.964 X 103) Step 1 - Add: 2.56 + 6.964 = 9.524 Step 2 – Bring down exponent : 9.524 x 103

Step 2 – Bring down exponent: Example 2 (9.49 X 105) – (4.863 X 105) Step 1 - Subtract: 9.49 – 4.863 = 4.627 Step 2 – Bring down exponent: 4.627 x 105

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 so that they will have the same exponent.

Moving the Decimal 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.

Adding/Subtracting when the Exponents are DIFFERENT Step 1 – Rewrite so the exponents are the same Step 2 - add/subtract the decimal Step 3 – Bring down the given exponent on the 10

Example 3 (2.46 X 106) + (3.4 X 103) Step 1 – Rewrite with the same exponents 3.4 X 103  0.0034 X 103+3 New Problem: (2.46 X 106) + (0.0034 X 106) Step 2 – Add decimals 2.46 + 0.0034 = 2.4634 Step 3 – Bring Down Exponents 2.4634 X 106

Example 4 (5.762 X 103) – (2.65 X 10-1) Step 1 – Rewrite with the same exponents 2.65 X 10-1  0.000265 X 10(-1+4) New Problem : (5.762 X 103) – (0.000265 X 103) Step 2 – Subtract Decimals 5.762 – 0.000265 = 5.762 Step 3 – Bring down decimals 5.762 X 103

Practice (3.45 x 103) + (6.11 x 103) (4.23 x 103) – (9.56 x 102)