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Significant Figures and Scientific Notation Ms. Cannon

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Accuracy versus Precision Accuracy – A measurement of how close a measurement comes to the _________ or _______ value Precision – A measure of how close a ________ of measurements are to one another; repeatable

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Accurate. The average is accurate, but NOT _________. Precise, but NOT __________. Accurate AND Precise!!

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Rules for Working With Significant Figures 1.All numbers from 1 to 9 are ALWAYS significant! Example: 3 ___ Sig Fig 2.Leading zeros are NEVER significant. Examples: 0.00061 ___ Sig Figs or 0284 ___ Sig Figs 3.Imbedded zeros are ALWAYS significant. Example: 60002 ___ Sig Figs or 1403 ___ Sig Figs 4.Trailing zeros are significant ONLY if the decimal point is specified. Example: 830 ___ Sig Figs 750. ___ Sig Figs 830.0 ___ Sig Figs

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Example Number of Significant Figures 0.00682 ___ Rule #2: Leading zeros are not significant. Example Number of Significant Figures 1.072 ___ Rule #3: Imbedded zeros are always significant.

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Example Number of Significant Figures 300 Rule #4: Trailing zeros are significant only if the decimal point is specified. Example Number of Significant Figures 300. 300.0

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Multiplication or Division: Round the answer to _______ number of significant figures as number with the _______ number of significant figures. Rules for Working With Significant Figures

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Addition or Subtraction: Round result to _______ number of decimal spaces as number with ______ decimal spaces.

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General Rule for Rounding General rule for rounding: If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number ______. – Example: 38 rounded to the nearest ten is 40 If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number _______. – Example: 33 rounded to the nearest ten is 30

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Exact and Inexact Numbers There are two kinds of numbers in the world: Exact Inexact Exact: – example: There are exactly 12 eggs in a dozen. – example: Most people have exactly 10 fingers and 10 toes.

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Exact and Inexact Numbers Inexact numbers: – Example: any measurement. – If I quickly measure the width of a piece of notebook paper, I might get 220 mm (2 significant figures). – If I am more precise, I might get 216 mm (3 significant figures). – An even more precise measurement would be 215.6 mm (4 significant figures).

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Scientific Notation In any effort to reduce the cumbersome nature of very large and very small numbers, scientists and engineers use ____________ ____________. This removes the problem of excessive leading and trailing ___________.

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Scientific Notation Standard Form _________._________ X 10 Exp. Ones Place.10th Place Example: 2.6 x 10 4

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How do you change a number into Scientific Notation? Example 1) 1047 Step 1: Find the decimal? At the end of the number _______ Step 2: Move the decimal to the left _______ (decimal moved ____ decimal places) Step 3: The exponent equals the number of decimal places and is positive because moved decimal to the left ______________ Rounds to _____________

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How do you change a number into Scientific Notation? Example 2) 0.00005432 Step 1: Find the decimal? At the beginning of the number 0.00005432 Step 2: Move the decimal to the right _________(decimal place moved ___ places) Step 3: The exponent equals the number of decimal places and is negative because moved decimal to the right ______________ Rounds to ___________

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Practice Problems Complete the following chart:

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