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Scientific Notation

Scientific Notation. Unit 1, Lesson 6. The Basics. Scientific Notation means expressing numbers (usually very large numbers or very small numbers) in the following form: a number between1 and 10 times 10 to an exponent such as: 2.3 X 10 4 4.76 X 10 -3

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Scientific Notation

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  1. Scientific Notation Unit 1, Lesson 6

  2. The Basics Scientific Notation means expressing numbers (usually very large numbers or very small numbers) in the following form: a number between1 and 10 times 10 to an exponent such as: 2.3 X 104 4.76 X 10 -3 12.3 X 109isn’t in scientific notation because 12.3 isn’t between 1 and 10

  3. Converting from Decimal to Scientific Notation Simple rule: moving a decimal to the “right” means the exponent is negative; moving to the “left” means the exponent is positive Ex. 1 Put 0.000458 into scientific notation: First, move the decimal to the right 4 places 4.58 Second, moving to the right means a neg. exponent and the exponent is the same as the places moved 4.58 x 10-4

  4. Converting from Decimal to Scientific Notation Ex. 2 Put 1,256,008 into scientific notation Note: every number has a decimal point; if the number is an integer, the decimal is at the end even if it isn’t written So for 1,256,008 the decimal is to the right of the 8 First, move the decimal to the left 6 places  1.256008 Second, moving to the left means a positive exponent 1.256008 X 106

  5. Converting from Scientific Notation to decimal form Same rule, just in reverse: If the exponent is negative, move the decimal to the left If the exponent is positive, move the decimal to the right Ex.1 3.06 X 10 -4 Negative exponent means move to the left (the number gets smaller); move decimal the same number of places as the exponent 3.06 X 10 -4 = .000306

  6. Converting from Scientific Notation to decimal form Ex. 2 Write 8.7103 X 108 in decimal form First, a positive exponent means the decimal will be moved to the right; the “number” gets bigger. Note: Add zeros as needed when moving the decimal 8.7103 X 108= 871,030,000

  7. Practice Write in Scientific notation • 0.00056 = 5.6 X 10-4 • 405 = 4.05 X 102 • 6741.38 = 6.74138 X 103 • .7065 = 7.065 X 10-1

  8. Practice Write in decimal form: • 3.07 X 10 -5 = .0000307 • 3.07 X 10 4 = 30,700

  9. Computing with Scientific Notation To multiply numbers written in scientific notation, keep in mind the rules for exponents: With same base (10 in this case), add the exponents. Ex. 1: Simplify (3.5 X 104)(6.7 X 10-3) First, multiply the 3.5 and 6.7 = 23.5 Second, add the exponents  104 X 10-3 = 101 Next, put them together  23.5 X 101 Finally, notice that the decimal needs to be moved and the exponent adjusted accordingly  2.35 X 102

  10. Computing with Scientific Notation To divide, it’s basically the same steps: Divide the numbers Subtract the exponents since they have the same base and are being divided (this is one of the rules for exponents) Adjust the size of the exponent as needed Ex: First, 5.8 ÷ 1.4 = 4.14 Second, subtract the exponents  4 - -5 = 4 + 5 = 9 Next, put it back together  4.14 X 109

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