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Published byRosamond Nash Modified over 6 years ago

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Sig Figs

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Scientific Notation In science, we often come across either very large or very small numbers, so we use Scientific Notation as a way to simplify them. Some numbers hard to work with: Mass of one atom = 0.000000000000000000000000000000091 kg # atoms in 2 grams of hydrogen = 1200000000000000000000000 atoms

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Scientific Notation Easier: Mass of one electron = 9.1 x 10 -32 # atoms in 2 g hydrogen = 1.2 x 10 24

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In Scientific Notation, a number is written as the product of two numbers: A coefficient, and 10 raised to a power (exponent). The coefficient is always greater than or equal to 1, and less than 10 M x 10 n M = Coefficient between 1 and 10 10 is the base n is the exponent

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Scientific Notation Worksheet Numbers > 1 have a positive exponent 5.2 x 10 3 Numbers < 1 have a negative exponent 9.65 x 10 -4

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The Importance of Measurement Ex: 2011. converted to scientific notation: In this case: In order for the coefficient to be between 1 and 10, the decimal has to move 3 places to the left. The decimal moved 3 times, so the value of the exponent is 3 The number (2011) is bigger than 1, so the exponent will be positive. (10 3 = 1000., so this reads 2.011 x 1000 which = 2011.) Ex: 0.036 converted to scientific notation: In this case: In order for the coefficient to be between 1 and 10, the decimal has to move 2 places to the right. The decimal moved 2 times, so the value of the exponent is 2 The number (0.036) is less than 1, so the exponent will be negative. (10 -2 = 0.01, so this reads 3.6 x 0.01 which = 0.036) 2.011x 10 3 + 3.6 x 10 -2

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The Importance of Measurement 1.420 x 10 -9 2 x 10 6 Convert the following numbers from standard to scientific notation 2 000 000.0.000 000 001 420 Convert the following numbers from scientific to standard notation 7.29 x 10 15 7 290 000 000 000 000. 9.25 x 10 -11 0.000 000 000 092 5 Practice

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Significant Figures We keep track of measurement accuracy through significant digits(Sig Digs) also called significant figures (Sig. Fig) A measurement is considered to be more accurate if it has more significant digits Significant Figures = all known digits plus one estimated digit

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Significant Figures RULES 1) No zeros? All significant. 377 2) All sandwich zeros significant. 307 3) Leading zeros are not significant. 0.00312 4) If digits are left of a decimal then zeros right of a decimal are significant3.00 5) Scientific notation indicates significant figures when numbers end in zero 300 = 3 x 10 2 or 3.00 x 10 2 When you have to guess, zeros don’t count

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Uncertainty in Measurements Practice: Count the number of significant digits in each measurement. 0.05730 meters8.750 x 10 -2 centimeters 8765 seconds 200. yards 0.00073 milliliters200 yards200.0 yards 40.070 grams101010 milliseconds 44 4 4 55 3 21

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Uncertainty in Measurements Accuracy is a measure of how close the measurement is to the actual, or “true value” of what was measured. Actual blood glucose level = 94.899 mg/dL

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Uncertainty in Measurements Precision is a measure of how close your measurements are to each other. -measurements do not have to be accurate to be precise -measurements can be both precise and accurate, or neither.

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