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Significant Figures Rules and Applications

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Rules for Determining Significant Figures 1.) All Non-Zero digits are Significant. 1.) All Non-Zero digits are Significant. For example: 134.987 m = SIX Significant Figures. For example: 134.987 m = SIX Significant Figures. 2.) All Zeros between two non-zero digits are significant. 2.) All Zeros between two non-zero digits are significant. For example: 10.006 cm = Five Significant Figures For example: 10.006 cm = Five Significant Figures

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More Rules 3.) All Zeros to the LEFT of an “Understood” decimal point but to the RIGHT of a Non-Zero Digit are NOT significant. 3.) All Zeros to the LEFT of an “Understood” decimal point but to the RIGHT of a Non-Zero Digit are NOT significant. For example: 178,000 ml = 3 Significant Figures For example: 178,000 ml = 3 Significant Figures

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More Rules 4.) All Zeros to the LEFT of an “Expressed” decimal point and to the RIGHT of a nonzero digit are Significant. 4.) All Zeros to the LEFT of an “Expressed” decimal point and to the RIGHT of a nonzero digit are Significant. For example: 178,000. g = six significant Figures. For example: 178,000. g = six significant Figures.

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More Rules 5.) All Zeros to the RIGHT of a decimal point but to the LEFT of a non-Zero digit are NOT significant. 5.) All Zeros to the RIGHT of a decimal point but to the LEFT of a non-Zero digit are NOT significant. For example: 0.00023 m = Two significant Figures For example: 0.00023 m = Two significant Figures

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More Rules 6.) All Zeros to the RIGHT of a decimal point AND to the RIGHT of a non-Zero digit are significant. 6.) All Zeros to the RIGHT of a decimal point AND to the RIGHT of a non-Zero digit are significant. For example: 0.0140 kg =Three significant Figures For example: 0.0140 kg =Three significant Figures

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Rule For Addition and Subtraction with S.F. 1.) Line up the numbers you wish to + or – by the decimal point. 1.) Line up the numbers you wish to + or – by the decimal point. 2.) Add or Subtract the numbers then write your answer to the same placement as the LEFT most LAST Significant DIGIT. 2.) Add or Subtract the numbers then write your answer to the same placement as the LEFT most LAST Significant DIGIT.

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Example: (+) Problem: 1.0521 g + 2.52 g 1.) Line up by Decimal Point 1.) Line up by Decimal Point 3.57 g (NOT = 3.5721 g) 3.57 g (NOT = 3.5721 g) 2.) Answer to the same placement as the LEFT most LAST Significant Digit 2.) Answer to the same placement as the LEFT most LAST Significant Digit 1.0521 g +2.52 g

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Rule For Multiplication and Division with S.F. 1.) Multiply or Divide the numbers. 1.) Multiply or Divide the numbers. 2.) Write your Product or Quotient so it has the same amount of Significant Figures as the number that had the LEAST amount of Significant Figures. 2.) Write your Product or Quotient so it has the same amount of Significant Figures as the number that had the LEAST amount of Significant Figures.

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Example: (x) Example: (x) Problem: 32.00 m x 1.015 m x 120 m 1.) Multiply the numbers 1.) Multiply the numbers = 3897.6 m 2.) Answer must have same amount of Sig. Figs. as number with the Least amount of Sig. Figs. 2.) Answer must have same amount of Sig. Figs. as number with the Least amount of Sig. Figs. 32.00 = 4 1.015 = 4 120 = 2 Answer must have 2 Sig. Figs: = 3900 m

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