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Significant Figures and Scientific Notation

Significant Figures and Scientific Notation. Significant Figures The numbers reported in a measurement are limited by the measurement tool. The more precise the tool, the better the measurement.

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Significant Figures and Scientific Notation

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  1. Significant Figures and Scientific Notation

  2. Significant Figures The numbers reported in a measurement are limited by the measurement tool. The more precise the tool, the better the measurement. Example: If you were measuring gold to turn in, would you want to measure it on your bathroom scale or an electronic scale? Why?

  3. There are THREE main rules to determining Significant Figures… Rule 1: Leading Zero’s never count 0.008mm 0.0156oz 0.0042lb 0.000262 mL

  4. Rule 2: Trailing zero’s only count if there is a decimal point. 25,000centimeters 200.Dollars 48,600gallons 25,005,000ounces

  5. Rule 3: All other numbers that are not leading or trailing zero’s count. 50.8 mm 2001 min 0.702 lb 0.00405m

  6. Your turn to practice! State the number of significant figures in each of the following: 0.030 m 4.050 L C. 0.0008 g D. 3.00 m E. 2,080,000 bees In which set do both numbers contain the same number of significant figures? 22.0 and 22.00 400.0 and 40 3) 0.000015 and 150,000

  7. Scientific Notation Is used for really, really, really small numbers or really, really, really large numbers. It is written as: The factor must be a number between 1 & 10 but not 10. Examples: 1.0, 2.4, 3.10, etc What would be the factor for the numbers below? 321 7,689 .00000483 .00211

  8. Scientific Notation * If your starting number is greater than 1, your exponent will be positive. 1,409, 325,000,000,000 1.409325 x 10 + * If your starting number is less than 1, your exponent will be negative. .000917 9.17 x 10 - * Next count the number of spots you had to move to make it a number between 1 & 10, but not ten. You had to move the decimal point 15 spaces from the very end to between the 1 & 4 to get a number between 1 & 10, but not 10. Therefore your exponent will be: +15 1,409, 325,000,000,000 1.409325 x 10 +15

  9. Now try these! .000917 9.17 x 10 - You should have gotten 9.17 x 10 -4 10.478 x 10 6 3.22 x 10 -3 2.59 x 10 5 4.6813 x 10 2 3.8 x 10 -13 1,478, 000 0.00322 259,000.00 468.13 .00000000000038 Remember: All numbers before the times sign are significant! 3.40 x 10 5 9.67 x 10 3 1.21 x 10 -7

  10. What if I need to go backwards from Scientific Notation to Standard Notation? Easy! Just add the number of zero’s needed to get your original factor back! 2.59 x 10 9 2,590,000,000 6.143 x 10 -8 .00006143 Remember that if your exponent is positive, you will add zeros to the right of the decimal. But, if your exponent is negative, you will add zero’s to the left of your decimal. Try these! 8.31 x 10 7 7.32 x 10 -13 4.67 x 10 -4 2.19 x 10 10

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