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Why Scientific Notation?

Why Scientific Notation?. A short-hand way of writing numbers without writing all of the zeros . Scientific Notation Video. How many protons are in the Sun if it’s made up entirely of protons?. Mass of the sun = 2 x 10 30 kg Mass of a proton = 1.673 x 10 -27 kg Video Answer.

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Why Scientific Notation?

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  1. Why Scientific Notation? A short-hand way of writing numbers without writing all of the zeros. Scientific Notation Video

  2. How many protons are in the Sun if it’s made up entirely of protons? • Mass of the sun = 2 x 1030 kg • Mass of a proton = 1.673 x 10-27 kg • Video Answer

  3. Using a Calculator (not a phone) • On a scientific calculator, scientific notation is done with the button. 1.5 x 108 is typed 1.5 8 • “EE” or “10x” are also used

  4. Scientific Notation to Standard Form Multiply by the power of ten • 3.4 x 105 in scientific notation • 3.4 x 100 000 (or 3.4 [exp] 5) • 340,000 in standard form

  5. Scientific Notation A number is expressed in scientific notation when it is in the form a x 10n where a is between 1 and 10 and n is an integer

  6. The Distance From the Sun to the Earth 150,000,000 km Write in scientific notation!

  7. Step 1 • Move decimal left • Leave only one number in front of decimal 150,000,000 = 1.50000000

  8. Step 2 • Write number without zeros 150,000,000 = 1.5

  9. 8 150,000,000 km = 1.5 x 10 km Step 3 • Count how many places you moved decimal • Make that your power of ten

  10. The power of ten is 8 because the decimal moved 8 places. 8 150,000,000 km= 1.5 x 10 km

  11. 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> 4.2 x 106 -----> Practice Problem Write in scientific notation. Decide the power of ten. • 98,500,000 = 9.85 x 10? • 64,100,000,000 = 6.41 x 10? • 279,000,000 = 2.79 x 10? • 4,200,000 = 4.2 x 10?

  12. Express 0.000 000 0902 in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10-8

  13. More Practice Problems Convert to Scientific Notation • 0.0734 = ______ • 0.870 = ______ • 0.009 = _______ • 0.00109 = _______ Answers • 7.34 x 10-2 2)8.70 x 10-1 3) 9 x 10-3 4) 1.09 x 10-3

  14. Express 1.8 x 10-4 in standard notation. 0.00 018 Express 4.58 x 106 in standard notation. 4 580 000

  15. More Practice Problems Convert to Scientific Notation • 734 000 000 = ______ • 870 000 000 000 = ______ • 90 000 000 000 = _______ Answers 3) 9 x 1010 • 7.34 x 108 2)8.7 x 1011

  16. More Practice Problems Convert to Scientific Notation with 3 significant digits • 9 026 100 000 = ______ • 0.007801 = ______ • 5 996 110 000 = _______ Answers 3) 6.00 x 109 • 9.03 x 109 2)7.80 x 10-3

  17. Converting Units • Use the given conversions and set up an equation • Convert 1500 m to km • We know 1km = 1000m, so set up the equation: 1km = __?_km__  0.001x1500 = 1.5 km 1000m 1500m

  18. Converting Lightyears • 1 light year = 9.5 x 1012 km • Use the following equation to convert ly to km and km to ly 1ly = ly__ 9.5 x 1012kmkm or 9.5 x 1012km= ____km __ 1ly ly

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