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Scientific Notation

Learn how to write large numbers in scientific notation and determine significant figures. Practice problems included.

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Scientific Notation

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

  2. The Distance From the Sun to the Earth 93,000,000

  3. Step 1 • Move decimal left for numbers more than one and right for numbers less than one • Leave only one number in front of decimal 93,000,000 = 9.3000000

  4. Step 2 • Write number without zeros 93,000,000 = 9.3

  5. Step 3 • Count how many places you moved decimal • Make that numbers your power of ten 93,000,000 = 9.3 X 107

  6. If you move the decimal to the right, the exponent (power of ten) will be a negative number. Ex: 0.00000345 = 3.45 x 10-6 • If you move the decimal to the left, the exponent (power of ten) will be a positive number. Ex: 280000000 = 2.8 x 108

  7. 2.79 x 108 Practice Problem Write in scientific notation. Decide the power of ten. • 98,500,000 = 9.85 x 10? • 0.0000308 = 3.08 x 10? • 279,000,000 = 2.79 x 10? • 0.00000093 = 9.3 x 10? 9.85 x 107 3.08 x 10-5 9.3 x 10-7

  8. More Practice Problems On these, decide where the decimal will be moved. • 734,000,000 = ______ x 108 • 870,000,000,000 = ______x 1011 • 0.00000000092 = _____ x 10-10 Answers 3) 9.2 x 10-10 • 7.34 x 108 2) 8.7 x 1011

  9. Complete Practice Problems Write in scientific notation. • 50,000 • 7,200,000 • 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

  10. Complete # 1 on your practice sheet.

  11. Scientific Notation to Standard Form • Add zeros to your number to match the exponents 1) 3.4 x 105 3.40000 x 105 2. Move the decimal to the right if the exponent is positive, and to the left if the exponent is negative = 340,000

  12. 6.27 x 106 9.01 x 104 = 6,270,000 = 90,100 Write in Standard Form

  13. Complete # 2 on your practice sheet.

  14. Significant Figures • A “significant figure” in a measured value is one that is known with certainty or can be reasonably estimated. How would you report the meter reading? How many significant figures does your answer have?

  15. What time is it? • Someone might say “1:30” or “1:28” or “1:27:55” • Each is appropriate for a different situation • In science we describe a value as having a certain number of “significant digits”

  16. Sig Fig Rules 523.7 has ____ significant figures 1. Non-zero digits are always significant. 2. Any zeros between two significant digits are significant. 23.07 has ____ significant figures 3. A final zero or trailing zeros in the decimal portion ONLY are significant. 3.200 has ____ significant figures 200 has ____ significant figures 2.00 x 102 has ____ significant figures

  17. Complete # 3 and 4 on your practice sheet.

  18. Adding and Subtracting The number of decimal places in the answers should be the same as in the measured quantity with the smallest number of decimal places. Examples: • a) 13.64 + 0.075 + 67 b) 267.8 – 9.36 13.64 267.8 + 0.075 – 9.36 + 67. 80.715 81 258.44

  19. Complete # 5 on your practice sheet.

  20. Multiplication and Division The number of significant figures in the answer should be the same number of significant digits as the value with the fewest number of significant digits. Example 608.3 x 3.45 Sig figs in 608.3? 4 Sig figs in 3.45? 3 So the answer will have ____ sig figs? 3 608.3 x 3.45 = 2098.635 = 2.10 x 103

  21. Complete # 6 on your practice sheet.

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