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Published byMarcia Cain Modified over 8 years ago

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**Adding and Subtracting Numbers in Scientific Notation**

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**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.

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**If the Exponents are the same:**

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

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

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

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**Adding/Subtracting when the Exponents are Different**

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**If the Exponents are different:**

Turn the expression into Standard Notation Calculate Turn the result back into Scientific Notation

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

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

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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.

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**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.

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**Need a Challenge?? …continued**

Remember!!! For each move of the decimal to the right, you have to add -1 to the exponent 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 = X 104

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**Need a Challenge?? …continued**

Same problem as before! Given: X 103 – 2.65 X 10-1 X 10(-1+4) Subtract: X X 103 X 103 Answer: X 103 Exponents don’t match! Shift decimal 4 places to the left for to become 103.

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**Need a Challenge?? …continued**

Same problem as before! Given: 2.46 X X 103 X 103+3 Add: 2.46 X X 106 Answer: X 106 Shift decimal 3 places to the left for 106. .

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**Need a Challenge?? …continued**

Try a new problem! Given: 7.4 X X 106 X 10(2+4) Add: X X 106 X 106 Answer: X 106 Shift decimal 4 places to the left for 106. .

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**Practice Worksheet (solve using either method)**

2 × × 104 = 7 × 105 – 5.2 × 104 = 3.4 x 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

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