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Opener:. When you’re taking notes, if you have to write the same big word or words over and over again….do you write it out every time? How do you make it quicker? If some random person looked at your notes would they be able to read them? Why or why not?.

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  1. Opener: • When you’re taking notes, if you have to write the same big word or words over and over again….do you write it out every time? How do you make it quicker? • If some random person looked at your notes would they be able to read them? Why or why not?

  2. Scientific NotationShorthand method of writing very large and very small numbers based on powers of 10

  3. For example:432600000000 = 4.326 x 10110.00000000134 = 1.34 x 10-9The decimal goes after the first whole numberThe superscript tells you how many decimal places to move, and in what direction.

  4. 7.3x104 = 7.3 x 10,000 = 73,000 • (to write the number out longhand, the decimal point moved 4 places to the right) 9.4x10 -3 = 9.4 x 0.001 = 0.0094 • ( to write the number out longhand, the decimal point moved 3 places to the left)

  5. Practice • Write the following numbers in scientific notation; 94,320,000,000 469,000,000,000,000,000,000 0.000000000948 (9 zeros after the decimal) 0.0000643 • Write the following numbers out the long way; 7.14 x 106 3.41 x 10 3 1.81 x 10 -5 8.96 x 10 -4

  6. Math with exponents When adding and subtracting numbers with exponents, you must first convert all numbers to have the same exponent. 1) 2.81x107 + 4.32x108 = 0.281x108 + 4.32x108 = 4.601x108

  7. 2) 9.32x1021 - 1.54x1020 =

  8. 2) 9.32x1021 - 1.54x1020 = 9.32x1021 - 0.154x1021 =

  9. 2) 9.32x1021 - 1.54x1020 = 9.32x1021 - 0.154x1021 = 9.166x1021

  10. When multiplying numbers with exponents, you simply multiply the coefficients and add the exponents. 3) (1.21x1014 )(3.42x1012) = (1.21 x 3.42) x10(14+12) = 4.14x1026

  11. When dividing numbers with exponents, you divide the coefficients and subtract the exponents. 4) (4.19x107) / (2.16x103) = (4.19/2.16) x10(7-3) = 1.94x104

  12. Now you try a few… 8.46x109+ 1.23x1011 = 9.84x1014- 6.18x1015 = (2.91x106)(4.33x104) = 7.94x1010 ∕ 3.24x103 =

  13. Closer: • List the steps involved in multiplying two numbers that have exponents. • How would those steps change if you were dividing the numbers instead?

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