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Significant Figures and Scientific Notation Ms. Cannon

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

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

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

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.

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

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

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

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

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.

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).

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 ___________.

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

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 _____________

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 ___________

Practice Problems Complete the following chart:

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