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Chapter 1 “Chemistry and You” ‘Significant Figures and Scientific Notation’

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Scientific Notation Numbers that are very large or very small are conveniently expressed in scientific notation.

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Scientific Notation There are two parts to scientific notation: The first part is the number 1 or a number between 1 and 10 The second part is x 10 n So 54 000 = 5.4 x 10 4 And 0.000 008 765 = 8.765 x 10 -6

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Scientific Notation + If the decimal point is moved to the left, the exponent is POSITIVE - If the decimal point is moved to the right, the exponent is NEGATIVE

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Scientific Notation Rules for calculations: Addition and subtraction: All values must have the SAME exponent before they can be added or subtracted: 4.5 x 10 6 – 2.3 x 10 5 = 45 x 10 5 – 2.3 x 10 5 = 42.7 x 10 5 = 4.27 x 10 6

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Scientific Notation Rules for calculations: Multiplication The numbers are multiplied and the exponents are ADDED (3.1 x 10 3 ) (5.01 x 10 4 ) = (3.1 x 5.01) x 10 4+3 = 16 x 10 7 = 1.6 x 10 8

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Scientific Notation Rules for Calculations Division The numbers are divided and the exponents are SUBTRACTED 7.63 x 10 3 = 7.63 x 10 3-4 8.6203 x 10 4 8.6203 = 0.885 x 10 -1 = 8.85 x 10 -2

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The number of significant figures in a measurement depends on the ability of the measuring device. Significant figures in a measurement include all the known digits plus one that is estimated. Significant Figures

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Calculations with Sig Figs When a calculation involves measurements with numbers that have different numbers of significant figures, the answer should have the same number of significant figures as the number with the LEAST, in the measurement.

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Rule 1 All non-zero figures are significant 523 grams 972,366 sec 25.61 moles 3 significant figures 6 significant figures 4 significant figures

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Rule 2 0’s in the MIDDLE of a number are ALWAYS significant 5082 meters 2.0008 liters 0.00800341 moles 4 significant figures 5 significant figures 6 significant figures

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Rule 3 0’s in the front of a number are NEVER significant 0.0032 kg 0.00000751 meters 0.00300305 liters 2 significant figures 3 significant figures 6 significant figures

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Rule 4 – Part 1 0’s at the END of a number are SOMETIMES significant ** Decimal Point PRESENT, 0’s ARE significant 2.000 Liters 0.000500 grams 0.0070300 moles 4 significant figures 3 significant figures 5 significant figures

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Rule 4 – Part 2 0’s at the END of a number are SOMETIMES significant ** Decimal Point ABSENT, 0’s are NOT significant 2000 L 550 meters 3,005,000 seconds 1 significant figure 2 significant figures 4 significant figures

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Scientific notation is the most reliable way of expressing a number to a given number of significant figures. In scientific notation, the power of ten is insignificant.

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For example, if one wishes to express the number 2000 to varying degrees of certainty: 2000 2 x 10 3 is expressed to one significant figure. 2000 2.0 x 10 3 is expressed to two significant figures. 2000 2.00 x 10 3 is expressed to three significant figures 2000 2.000 x 10 3 is expressed to four significant figures

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Rounding Off Significant figures When rounding, examine the figure following (i.e., to the right of) the figure that is to be last. This figure you are examining is the first to be dropped.

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The Rules 1.If it is less than 5, drop it and all the figures to the right of it. 2.If is more than 5, increase by 1 the number to be rounded, that is, the preceding figure. 3.If it is 5, round the number so that is will be even.

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Example1 Round 62.5347 to four significant figures. Look at the 5 th figure. It is a 4 A number less than 5. Drop every figure after the fourth The original number rounds to 62.53

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Example 2 Round 3.78721 to three significant figures Look at the 4 th figure. It is 7. A number greater than 5. Round the original number up. The original number rounds to 3.79

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Example 3 Round 726.835 to five significant figures. Look at the 6 th figure. It is 5. Now look at the 5 th figure. It is 3. ODD Round the original number up. The original number rounds to 726.84

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Example 4 Round 24.85 to three significant figures. Look at the 4 th figure. It is 5. Now look at the 3 rd figure. It is 8. EVEN Drop the 5 and all number after it. The original number rounds to 24.8

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