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Dividing with Scientific Notation How can we deal with so many zeros? The mass of one carbon atom = 12.01 602,200,000,000,000,000,000,000 Covered in this lesson • This lesson demonstrates how to divide with scientific notation. – Scientific notation can be divided easily with or without a calculator when the factors (the number between 1 and 10) and exponents (power of ten) are considered. Scientific Notation • All scientific notation is expressed with a factor multiplied by a power of 10. • Examples A. 5.89 X 107 m C. 9.00 X 10-3g B. 3.0 X 1018 dL D. 7.1 X 10 -12Mm Methods of Dividing • There are at least two methods you can use to divide in scientific notation. –The short hand way using a scientific calculator. –The long hand way without a scientific calculator. Using a Scientific Calculator • If you are dividing in scientific notation use the following method. –Enter the first number in ( ) divided by the second number in ( ) –Press enter (Note the power of 10 will be given the symbol exp) Example: Scientific Calculator • (1.47 X 107) / (6.00 X 1010) = • Put the first number in ( ) divide by the second number in ( ) It looks like this (1.47*10^7)/(6.00*10^10) Press enter you see Write your answer 2.45exp-4 2.45 X 10-4 2nd Method Using a Scientific Calculator • Use the exp key dividing as usual. • Enter the numbers as follows: – first number: factor, exp key, exponent – divide – second number: factor, exp key, exponent – Enter Example: 2nd Method Scientific Calculator • (1.47 X 107) / (6.00 X 1010) = • Use the exp key and just divide. It looks like this 1.47exp7/6.00exp10 Press enter you see 2.45exp-4 Write your answer 2.45 X 10-4 Example: Without Calculator • Divide the factors • Subtract the power of 10 exponents • Put them together • Change back to scientific notation. Without Calculator Example • (1.47 X 107) / (6.00 X 1010) = • Divide the factors 1.47/6.00 = 0.245 7 - 10 = -3 • Subtract the exponents • Put them together 0.245 X 10-3 • change back to scientific notation. = 2.45 X 10-4 the final answer Practice problems 1. (6.38 X 109) / (7.83 X 105) = 2. (2.038 X 107) / (2.00 X 10-11) = 3. (5.89 X 10-5) / (3.0 X 1010) = 4. (9.00 X 10-8) / (7.1 X 10 -4) = Answers Practice Problems 1. 8.15 X 103 2. 102 X 106 3. 1.96 X 10-15 4. 1.27 X 10-4