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Chem Lecture Notes Sept 3 Nums

Chem Lecture Notes Sept 3 Nums - Numbers Several types of...

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Numbers Several types of numbers: integer, real rational, real irrational and complex (not used in CHE100). Measured numbers have a precision that is limited by the experimental apparatus. Manipulating such numbers requires a knowledge of significant figures. Scientists often use standard scientific notation for numbers.
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Examples of Numbers Integers: ..., -2, -1, 0, 1, 2, ... Real rational: integer/integer (1.2 = 6/5) Pi = 3.14159... (can’t be written as n/m) Standard Scientific notation: 123.456=1.23456X10 2, .000123=1.23X10 -4 There is always one non zero digit to the left of the decimal point.
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What is a Measurement? quantitative observation comparison to an agreed upon standard every measurement has a number and a unit
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A Measurement the unit tells you what standard you are comparing your object to the number tells you 1.what multiple of the standard the object measures 2.the uncertainty in the measurement
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Scientists have measured the average global temperature rise over the past century to be 0.6°C °C tells you that the temperature is being compared to the Celsius temperature scale 0.6 tells you that 1. the average temperature rise is 0.6 times the standard unit 2. the uncertainty in the measurement is such that we know the measurement is between 0.5 and 0.7°C
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Numerical Precision Apparatus dependence: measuring length with a yardstick with only foot markings versus one with inch markings. Inherently limited precision: How tall you are to the nearest hundredth of an inch depends on when the measurement was done and such things as how your hair is combed.
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Big and Small Numbers We commonly measure objects that are many times larger or smaller than our standard of comparison Writing large numbers of zeros is tricky and confusing not to mention the 8 digit limit of your calculator! the sun’s diameter is 1,392,000,000 m an atom’s average diameter is 0.000 000 000 3 m
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Scientific Notation each decimal place in our number system represents a different power of 10 scientific notation writes the numbers so they are easily comparable by looking at the power of 10 the sun’s diameter is 1.392 x 10 9 m an atom’s average diameter is 3 x 10 -10 m
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Exponents when the exponent on 10 is positive, it means the number is that many powers of 10 larger sun’s diameter = 1.392 x 10 9 m = 1,392,000,000 m when the exponent on 10 is negative, it means the number is that many powers of 10 smaller avg. atom’s diameter = 3 x 10 -10 m = 0.0000000003 m
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Scientific Notation To Compare Numbers Written in Scientific Notation First Compare Exponents on 10 If Exponents Equal, Then Compare Decimal Numbers 1.23 x 10 -8 decimal part exponent part exponent 1.23 x 10 5 > 4.56 x 10 2 4.56 x 10 -2 > 7.89 x 10 -5 10 10
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Writing Numbers in Scientific Notation 1 Locate the Decimal Point 2 Move the decimal point to the right of the first non-zero digit from the left n
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12340 1 Locate the Decimal Point 12340 .
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