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Scientific Notation

Scientific Notation. Finish these equations. 7000 = 7 x 10 n. 3. 600,000 = 6 x 10 n. 5. 30,000,000 = 3 x 10 n. 7. 1.47 x 100 =. 147. 82 x 10,000 =. 820,000. 0.0629 x 1000 =. 62.9. Scientists use easy ways to write large numbers. This easy way is more compact & more useful.

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Scientific Notation

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  1. Scientific Notation

  2. Finish these equations 7000 = 7 x 10n 3 600,000 = 6 x 10n 5 30,000,000 = 3 x 10n 7 1.47 x 100 = 147 82 x 10,000 = 820,000 0.0629 x 1000 = 62.9

  3. Scientists use easy ways to write large numbers. This easy way is more compact & more useful. Scientific Notation This compact, useful method is called To write a number in Scientific Notation, express it as a product of two factors There are 2 criteria for writing a number in Scientific Notation:

  4. Criteria: • One factor is a number GREATER than or EQUAL to 1, butLESS than 10. (This will usually be a decimal) • b. The other factor is a POSITIVE POWER of 10. • Let’s look at an example: 93,000,000 Notice that the decimal point is moved until it reaches a number greater than 1, but less than 10.

  5. How many times was the decimal point moved to the left? That answer is your exponent. 93,000,000 in Scientific Notation is: 9.3 x 107 Steps: 1. Move the decimal point to the LEFT until you get to a number greater than or equal to 1, but less than 10. 2. Count the number of places moved- that is the power of 10.

  6. Another example: 185,000 1.85 x 105 Let’s try some: 120,000 1.2 x 105 4,064,000 4.064 x 106 25,000 2.5 x 104 714,500 7.145 x 105 1.56 x 108 156,000,000

  7. How would you reverse Scientific Notation (write in standard form)? • Do the OPPOSITE. • Move the decimal point the number of places as the exponent in the Power of 10 to the RIGHT. • 2. Add 0’s as place fillers. 3.6 x 103 3,600

  8. Let’s try some 9.07 x 104 90,700 9 x 105 900,000 1.9 x 104 19,000 7.005 x 107 70,050,000 9.415 x 108 941,500,000

  9. Scientific Notation can also be used to rename large decimals that are between 0 & 1 These numbers will use negative exponents for their powers of 10. Let’s look at an example: • Follow these rules: • First factor is greater than 1, but less than 10. • 2. Second factor is a power of 10 with a negative exponent. The exponent depends on how many times you moved the decimal to the RIGHT. 0.00064= 6.4 x 10-4

  10. Here’s another example: 0.0815 = 8.15 x 10-2 You try some: 0.015 = 0.0000086= 0.000124= 0.0069= 1.5 x 10-2 8.6 x 10-6 1.24 x 10-4 6.9 x 10-3

  11. 0.00000079 = 0.0000716 = 0.0045 = 7.9 x 10-7 7.16 x 10-5 4.5 x 10-3 It is now your turn to explain how to write numbers in scientific notation. Explain the process of scientific notation to the person next to you. Explain it using whole numbers & decimal between 0 & 1. Pretend that your partner does not understand this process, so explain it well & with examples!

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