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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. Example: If you were measuring gold to turn in, would you want to measure it on your bathroom scale or an electronic scale? Why? There are THREE main rules to determining Significant Figures… 0.008 mm 0.0156 oz 0.0042 lb 0.000262 mL 25,000 centimeters 200. Dollars 48,600 gallons 25,005,000 ounces 50.8 mm 2001 min 0.702 lb 0.00405 m State the number of significant figures in each of the following: A. 0.030 m B. 4.050 L C. 0.0008 g D. 3.00 m In which set do both numbers contain the same number of significant figures? E. 2,080,000 bees 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000 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 .00000483 7,689 .00211 * 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. 1,409, 325,000,000,000 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 1.409325 x 10 +15 .000917 9.17 x 10 - You should have gotten 9.17 x 10 -4 1,478, 000 10.478 x 10 6 0.00322 3.22 x 10 -3 259,000.00 2.59 x 10 5 3.40 x 10 5 4.6813 x 10 2 9.67 x 10 3 468.13 .00000000000038 3.8 x 10 -13 Remember: All numbers before the times sign are significant! 1.21 x 10 -7 Easy! Just add the number of zero’s needed to get your original factor back! 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. 2.59 x 10 9 2,590,000,000 6.143 x 10 -8 .00006143 Try these! 8.31 x 10 7 7.32 x 10 -13 4.67 x 10 -4 2.19 x 10 10