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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 2.46 X 103 + 3.476 X 103 or subtracting numbers in scientific notation, the exponents must be the same. 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: 1. Turn the expression into Standard Notation 2. Calculate 3. 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 Same problem as before! Need a Challenge?? …continued Given: 5.762 X 103 – 2.65 X 10-1 Shift decimal 4 places to the left for 10-1 to become 103. Exponents don’t match! .000265 X 10(-1+4) Subtract: 5.762 X 103- .000265 X 103 5.762 - .000265 X 103 Answer: 5.761735 X 103 Same problem as before! Need a Challenge?? …continued Given: 2.46 X 106 + 3.476 X 103 Shift decimal 3 places to the left for 106. . .003476 X 103+3 Add: 2.46 X 106 + .003476 X 106 Answer: 2.463476 X 106 Try a new problem! Need a Challenge?? …continued Given: 7.4 X 102 + 2.735 X 106 .00074 X 10(2+4) Shift decimal 4 places to the left for 106. . Add: .00074 X 106 + 2.735 X 106 .00074 + 2.735 X 106 Answer: 2.73574 X 106 Practice Worksheet (solve using either method) 1. 2. 3. 4. 2 × 103 + 3.6 × 104 = 3.8 x 104 7 × 105 – 5.2 × 104 = 6.48 x 105 3.4 x 102 + 4.57 x 103 = 4.91 x 103 8.41 x 10-5 – 7.9 x 10-6 = 7.62 x 10-5