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Measurement and Significant Digits....

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Measurement and Significant Digits >>>>>>>>>>>>>>>>>>>>> object | | | | cm ruler How do we record the length of this object? Length of object = 12.2 or 12.3 cm
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Measurement and Significant Digits >>>>>>>>>>>>>>>>>>>>> object | | | | cm ruler How do we record the length of this object? Length of object = _________________ cm ? Measurement and Significant Digits >>>>>>>>>>>>>>>>>>>>> object | | | | cm ruler How do we record the length of this object? Length of object = 12.2 or 12.3 cm Measurement and Significant Digits >>>>>>>>>>>>>>>>>>>>> object | | | | cm ruler How do we record the length of this object? Length of object = 12.2 or 12.3 cm = 12.3 0.1 cm Measurement and Significant Digits >>>>>>>>>>>>>>>>>>>>> object | | | | cm ruler How do we record the length of this object? Length of object = 12.2 or 12.3 cm = 12.3 0.1 cm Recorded measured quantities include only digits known for certain plus only one estimated or uncertain digit. Measurement and Significant Digits >>>>>>>>>>>>>>>>>>>>> object | | | | cm ruler How do we record the length of this object? Length of object = 12.2 or 12.3 cm = 12.3 0.1 cm Recorded measured quantities include only digits known for certain plus only one estimated or uncertain digit. These digits are called Significant Digits (Figures) or simply sigs or sig figs Significant Digits when recording measurements, physicists only record the digits that they know for sure plus only one uncertain digit Significant Digits when recording measurements, physicists only record the digits that they know for sure plus only one uncertain digit reflect the accuracy of a measurement Significant Digits when recording measurements, physicists only record the digits that they know for sure plus only one uncertain digit reflect the accuracy of a measurement Depends on many factors: apparatus used, skill of experimenter, number of measurements... Rules for counting sigs 1) s Rules for counting sigs 1) s 3 significant figures or 3 digit accuracy Rules for counting sigs 1) s 3 significant figures or 3 digit accuracy Leading zeros don't count. Start counting sigs with the first non-zero digit going left to right. Rules for counting sigs 1) s 3 significant figures or 3 digit accuracy Leading zeros don't count. Start counting sigs with the first non-zero digit going left to right. 2) kg Rules for counting sigs 1) s 3 significant figures or 3 digit accuracy Leading zeros don't count. Start counting sigs with the first non-zero digit going left to right. 2) kg 5 significant digits or 5 digit accuracy Rules for counting sigs 1) s 3 significant figures or 3 digit accuracy Leading zeros don't count. Start counting sigs with the first non-zero digit going left to right. 2) kg 5 significant digits or 5 digit accuracy Zeros between non-zero digits do count. Rules for counting sigs 1) s 3 significant figures or 3 digit accuracy Leading zeros don't count. Start counting sigs with the first non-zero digit going left to right. 2) kg 5 significant digits or 5 digit accuracy Zeros between non-zero digits do count. 3) N Rules for counting sigs 1) s 3 significant figures or 3 digit accuracy Leading zeros don't count. Start counting sigs with the first non-zero digit going left to right. 2) kg 5 significant digits or 5 digit accuracy Zeros between non-zero digits do count. 3) N4 digit accuracy or 4 sig figs Rules for counting sigs 1) s 3 significant figures or 3 digit accuracy Leading zeros don't count. Start counting sigs with the first non-zero digit going left to right. 2) kg 5 significant digits or 5 digit accuracy Zeros between non-zero digits do count. 3) N4 digit accuracy or 4 sig figs Trailing zeros to the right of the decimal do count. A Tricky Counting Sigs Rule m/s A Tricky Counting Sigs Rule m/s Not sure how many sigs: Ambiguous A Tricky Counting Sigs Rule m/s Not sure how many sigs: Ambiguous Must write quantities with trailing zeros to the left of the decimal in scientific notation. A Tricky Counting Sigs Rule m/s Not sure how many sigs: Ambiguous Must write quantities with trailing zeros to the left of the decimal in scientific notation. 8 X 10 3 m/s 8.0 X 10 3 m/s 8.00 X 10 3 m/s X 10 3 m/s A Tricky Counting Sigs Rule m/s Not sure how many sigs: Ambiguous Must write quantities with trailing zeros to the left of the decimal in scientific notation. 8 X 10 3 m/s1 significant figure 8.0 X 10 3 m/s 8.00 X 10 3 m/s X 10 3 m/s A Tricky Counting Sigs Rule m/s Not sure how many sigs: Ambiguous Must write quantities with trailing zeros to the left of the decimal in scientific notation. 8 X 10 3 m/s1 significant figure 8.0 X 10 3 m/s 2 significant digits 8.00 X 10 3 m/s X 10 3 m/s A Tricky Counting Sigs Rule m/s Not sure how many sigs: Ambiguous Must write quantities with trailing zeros to the left of the decimal in scientific notation. 8 X 10 3 m/s1 significant figure 8.0 X 10 3 m/s 2 significant digits 8.00 X 10 3 m/s3 sigs X 10 3 m/s A Tricky Counting Sigs Rule m/s Not sure how many sigs: Ambiguous Must write quantities with trailing zeros to the left of the decimal in scientific notation. 8 X 10 3 m/s1 significant figure 8.0 X 10 3 m/s 2 significant digits 8.00 X 10 3 m/s3 sigs X 10 3 m/s4 sig figs or 4 digit accuracy A Tricky Counting Sigs Rule m/s Not sure how many sigs: Ambiguous Must write quantities with trailing zeros to the left of the decimal in scientific notation. 8 X 10 3 m/s1 significant figure 8.0 X 10 3 m/s 2 significant digits 8.00 X 10 3 m/s3 sigs X 10 3 m/s4 sig figs or 4 digit accuracy In grade 12, assume given data with trailing zeros to the left of the decimal are significant...not true in general Accuracy vs Precision Accuracy Precision Accuracy vs Precision Accuracy tells us how close a measurement is to the actual or accepted value Precision Accuracy vs Precision Accuracy tells us how close a measurement is to the actual or accepted value Precision tells us how close repeated measurements of a quantity are to each other Accuracy vs Precision Accuracy tells us how close a measurement is to the actual or accepted value Depends on many factors: experiment design, apparatus used, skill of experimenter, number of measurements... Precision tells us how close repeated measurements of a quantity are to each other Accuracy vs Precision Accuracy tells us how close a measurement is to the actual or accepted value Depends on many factors: experiment design, apparatus used, skill of experimenter, number of measurements... Precision tells us how close repeated measurements of a quantity are to each other Depends on how finely divided or closely spaced the measuring instrument is...mm ruler is more precise than cm ruler More on Accuracy vs Precision Accuracy Reflected in the number of significant digits Precision More on Accuracy vs Precision Accuracy Reflected in the number of significant digits Precision Reflected in the number of decimal places Accuracy and Precision: A Golf Analogy * * * * * * * * * *hole* * * * * * ** * * * * * Red golfer = Blue golfer = Green golfer = Accuracy and Precision: A Golf Analogy * * * * * * * * * *hole* * * * * * ** * * * * * Red golfer = good precision and poor accuracy Blue golfer = Green golfer = Accuracy and Precision: A Golf Analogy * * * * * * * * * *hole* * * * * * ** * * * * * Red golfer = good precision and poor accuracy Blue golfer = poor precision and poor accuracy Green golfer = Accuracy and Precision: A Golf Analogy * * * * * * * * * *hole* * * * * * ** * * * * * Red golfer = good precision and poor accuracy Blue golfer = poor precision and poor accuracy Green golfer = good precision and good accuracy Formula Numbers are found in mathematics and physics equations and formulas Formula Numbers are found in mathematics and physics equations and formulas are not measured quantities and therefore are considered as exact numbers with an infinite number of significant digits Formula Numbers are found in mathematics and physics equations and formulas are not measured quantities and therefore are considered as exact numbers with an infinite number of significant digits Examples: red symbols are formula numbers d=2rC=2rT=2 (l/g) Eff%=W out /W in X 100 Weakest Link Rule for Multiplying and Dividing Measured Quantities Example:A rectangular deck is m long and 3.09 m wide. Find the area of the rectangular deck. Weakest Link Rule for Multiplying and Dividing Measured Quantities Example:A rectangular deck is m long and 3.09 m wide. Find the area of the rectangular deck A=L X W Weakest Link Rule for Multiplying and Dividing Measured Quantities Example:A rectangular deck is m long and 3.09 m wide. Find the area of the rectangular deck A=L X W =(2.148m)(3.09m) Weakest Link Rule for Multiplying and Dividing Measured Quantities Example:A rectangular deck is m long and 3.09 m wide. Find the area of the rectangular deck A=L X W =(2.148m)(3.09m) = m 2 Weakest Link Rule for Multiplying and Dividing Measured Quantities Example:A rectangular deck is m long and 3.09 m wide. Find the area of the rectangular deck A=L X W =(2.148m)(3.09m) = m 2 = =6.64 m 2 Weakest Link Rule for Multiplying and Dividing Measured Quantities Example:A rectangular deck is m long and 3.09 m wide. Find the area of the rectangular deck A=L X W =(2.148m)(3.09m) = m 2 = =6.64 m 2 Rule: When multiplying or dividing or square rooting, round the final answer to the same number of sigs as the least accurate measured quantity in the calculation. Weakest Link Rule for Adding and Subtracting Measured Quantities Example:A rectangular deck is m long and 3.09 m wide. Find the perimeter of the rectangular deck Weakest Link Rule for Adding and Subtracting Measured Quantities Example:A rectangular deck is m long and 3.09 m wide. Find the perimeter of the rectangular deck P = 2(L + W) Weakest Link Rule for Adding and Subtracting Measured Quantities Example:A rectangular de

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