Adding and Subtracting Numbers in Scientific Notation

Adding/Subtracting when Exponents are Equal When the exponents are the same: easy peasy: just add/subtract the numbers then carry the base 10 and the exponent through.

If the Exponents are the same: When adding or subtracting numbers in scientific notation, the exponents must be the same. 2.46 X 103 + 3.476 X 103 2.46 X 103 + 3.476 X 103 2.46 + 3.476 X 103 Then just rearrange the numbers and carry through the Power of 10

Example 1 2.56 X 103 + 6.964 X 103 Given: 2.56 X 103 + 6.964 X 103 2.56 + 6.964 = 9.524 Answer: 9.524 X 103

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

Adding/Subtracting when the Exponents are Different

If the Exponents are different: Turn the expression into Standard Notation Calculate Turn the result back into Scientific Notation

Example 1 Given: 2.46 X 106 + 3.476 X 103 Turn problem into Standard Notation: 2.46 X 106 = 2,460,000 3.476 X 103 = 3,476 Calculate: 2,460,000 + 3,476 = 2,463,476 Turn answer into Scientific Notation: 2.463476 X 106

Example 2 Given: 5.762 X 103 – 2.65 X 10-1 Turn problem into Standard Notation: 5.762 X 103 = 5,762 2.65 X 10-1 = .265 Calculate: 5,762 - .265 = 5761.735 Turn answer into Scientific Notation: 5.761735 X 103

Need a Challenge?? (You can skip this part if you want and do the problems at the end) When adding or subtracting numbers in scientific notation, the exponents must be the same. Therefore………… If they are different, you must move the decimal either right or left so that they will have the same exponent.

Need a Challenge?? …continued It does not matter which number you use to change the exponent, but remember that before you can do the calculation, both Powers of 10 have to have the same exponent on the 10.

Need a Challenge?? …continued Remember!!! For each move of the decimal to the right, you have to add -1 to the exponent. 0.3 X 103 = 3.0 X 102 For each move of the decimal to the left, you have to add +1 to the exponent. 0.3 X 103 = 0.03 X 104

Need a Challenge?? …continued Same problem as before! Given: 5.762 X 103 – 2.65 X 10-1 .000265 X 10(-1+4) Subtract: 5.762 X 103- .000265 X 103 5.762 - .000265 X 103 Answer: 5.761735 X 103 Exponents don’t match! Shift decimal 4 places to the left for 10-1 to become 103.

Need a Challenge?? …continued Same problem as before! Given: 2.46 X 106 + 3.476 X 103 .003476 X 103+3 Add: 2.46 X 106 + .003476 X 106 Answer: 2.463476 X 106 Shift decimal 3 places to the left for 106. .

Need a Challenge?? …continued Try a new problem! Given: 7.4 X 102 + 2.735 X 106 .00074 X 10(2+4) Add: .00074 X 106 + 2.735 X 106 .00074 + 2.735 X 106 Answer: 2.73574 X 106 Shift decimal 4 places to the left for 106. .

Practice Worksheet (solve using either method) 2 × 103 + 3.6 × 104 = 7 × 105 – 5.2 × 104 = 3.4 x 102 + 4.57 x 103 = 8.41 x 10-5 – 7.9 x 10-6 = 3.8 x 104 6.48 x 105 4.91 x 103 7.62 x 10-5