Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object...
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Transcript of Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object...
![Page 1: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/1.jpg)
Measurement and Significant Digits
![Page 2: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/2.jpg)
Measurement and Significant Digits
>>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length of this object?Length of object = _________________ cm ?
![Page 3: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/3.jpg)
Measurement and Significant Digits
>>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length of this object?Length of object = 12.2 or 12.3 cm
![Page 4: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/4.jpg)
Measurement and Significant Digits
>>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length of this object?Length of object = 12.2 or 12.3 cm = 12.3 ± 0.1 cm
![Page 5: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/5.jpg)
Measurement and Significant Digits
>>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length of this object?Length of object = 12.2 or 12.3 cm = 12.3 ± 0.1 cmRecorded measured quantities include only digits
known for certain plus only one estimated or uncertain digit.
![Page 6: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/6.jpg)
Measurement and Significant Digits
>>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length of this object?Length of object = 12.2 or 12.3 cm = 12.3 ± 0.1 cmRecorded 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”
![Page 7: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/7.jpg)
Significant Digits
when recording measurements, physicists only record the digits that they know for sure plus only one uncertain digit
![Page 8: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/8.jpg)
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
![Page 9: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/9.jpg)
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...
![Page 10: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/10.jpg)
Rules for counting sigs
![Page 11: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/11.jpg)
Rules for counting sigs
1) 0.00254 s
![Page 12: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/12.jpg)
Rules for counting sigs
1) 0.00254 s 3 significant figures or 3 digit accuracy
![Page 13: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/13.jpg)
Rules for counting sigs
1) 0.00254 s 3 significant figures or 3 digit accuracyLeading zeros don't count. Start counting sigs with the
first non-zero digit going left to right.
![Page 14: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/14.jpg)
Rules for counting sigs
1) 0.00254 s 3 significant figures or 3 digit accuracyLeading zeros don't count. Start counting sigs with the
first non-zero digit going left to right.2) 1004.6 kg
![Page 15: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/15.jpg)
Rules for counting sigs
1) 0.00254 s 3 significant figures or 3 digit accuracyLeading zeros don't count. Start counting sigs with the
first non-zero digit going left to right.2) 1004.6 kg 5 significant digits or 5 digit accuracy
![Page 16: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/16.jpg)
Rules for counting sigs
1) 0.00254 s 3 significant figures or 3 digit accuracyLeading zeros don't count. Start counting sigs with the
first non-zero digit going left to right.2) 1004.6 kg 5 significant digits or 5 digit accuracyZeros between non-zero digits do count.
![Page 17: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/17.jpg)
Rules for counting sigs
1) 0.00254 s 3 significant figures or 3 digit accuracyLeading zeros don't count. Start counting sigs with the
first non-zero digit going left to right.2) 1004.6 kg 5 significant digits or 5 digit accuracyZeros between non-zero digits do count.3) 35.00 N
![Page 18: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/18.jpg)
Rules for counting sigs
1) 0.00254 s 3 significant figures or 3 digit accuracyLeading zeros don't count. Start counting sigs with the
first non-zero digit going left to right.2) 1004.6 kg 5 significant digits or 5 digit accuracyZeros between non-zero digits do count.3) 35.00 N 4 digit accuracy or 4 sig figs
![Page 19: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/19.jpg)
Rules for counting sigs
1) 0.00254 s 3 significant figures or 3 digit accuracyLeading zeros don't count. Start counting sigs with the
first non-zero digit going left to right.2) 1004.6 kg 5 significant digits or 5 digit accuracyZeros between non-zero digits do count.3) 35.00 N 4 digit accuracy or 4 sig figsTrailing zeros to the right of the decimal do count.
![Page 20: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/20.jpg)
A “Tricky” Counting Sigs Rule
![Page 21: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/21.jpg)
A “Tricky” Counting Sigs Rule
4. 8000 m/s
![Page 22: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/22.jpg)
A “Tricky” Counting Sigs Rule
4. 8000 m/s Not sure how many sigs: Ambiguous
![Page 23: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/23.jpg)
A “Tricky” Counting Sigs Rule
4. 8000 m/s Not sure how many sigs: Ambiguous Must write quantities with trailing zeros to the left of
the decimal in scientific notation.
![Page 24: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/24.jpg)
A “Tricky” Counting Sigs Rule
4. 8000 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 103 m/s 8.0 X 103 m/s 8.00 X 103 m/s 8.000 X 103 m/s
![Page 25: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/25.jpg)
A “Tricky” Counting Sigs Rule
4. 8000 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 103 m/s 1 significant figure 8.0 X 103 m/s 8.00 X 103 m/s 8.000 X 103 m/s
![Page 26: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/26.jpg)
A “Tricky” Counting Sigs Rule
4. 8000 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 103 m/s 1 significant figure 8.0 X 103 m/s 2 significant digits 8.00 X 103 m/s 8.000 X 103 m/s
![Page 27: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/27.jpg)
A “Tricky” Counting Sigs Rule
4. 8000 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 103 m/s 1 significant figure 8.0 X 103 m/s 2 significant digits 8.00 X 103 m/s 3 sigs 8.000 X 103 m/s
![Page 28: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/28.jpg)
A “Tricky” Counting Sigs Rule
4. 8000 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 103 m/s 1 significant figure 8.0 X 103 m/s 2 significant digits 8.00 X 103 m/s 3 sigs 8.000 X 103 m/s 4 sig figs or 4 digit accuracy
![Page 29: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/29.jpg)
A “Tricky” Counting Sigs Rule
4. 8000 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 103 m/s 1 significant figure 8.0 X 103 m/s 2 significant digits 8.00 X 103 m/s 3 sigs 8.000 X 103 m/s 4 sig figs or 4 digit accuracyIn grade 12, assume given data with trailing zeros to the
left of the decimal are significant...not true in general
![Page 30: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/30.jpg)
Accuracy vs Precision
Accuracy Precision
![Page 31: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/31.jpg)
Accuracy vs Precision
Accuracy tells us how close a
measurement is to the actual or accepted value
Precision
![Page 32: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/32.jpg)
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
![Page 33: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/33.jpg)
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
![Page 34: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/34.jpg)
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
![Page 35: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/35.jpg)
More on Accuracy vs Precision
Accuracy Reflected in the number
of significant digits
Precision
![Page 36: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/36.jpg)
More on Accuracy vs Precision
Accuracy Reflected in the number
of significant digits
Precision Reflected in the number
of decimal places
![Page 37: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/37.jpg)
Accuracy and Precision: A Golf Analogy
![Page 38: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/38.jpg)
Accuracy and Precision: A Golf Analogy
* * * * * * * * * * hole * * * * * * *@* * * * * * * *Red golfer = Blue golfer =Green golfer =
![Page 39: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/39.jpg)
Accuracy and Precision: A Golf Analogy
* * * * * * * * * * hole * * * * * * *@* * * * * * * *Red golfer = good precision and poor accuracy Blue golfer =Green golfer =
![Page 40: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/40.jpg)
Accuracy and Precision: A Golf Analogy
* * * * * * * * * * hole * * * * * * *@* * * * * * * *Red golfer = good precision and poor accuracy Blue golfer = poor precision and poor accuracyGreen golfer =
![Page 41: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/41.jpg)
Accuracy and Precision: A Golf Analogy
* * * * * * * * * * hole * * * * * * *@* * * * * * * *Red golfer = good precision and poor accuracy Blue golfer = poor precision and poor accuracyGreen golfer = good precision and good accuracy
![Page 42: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/42.jpg)
Formula Numbers
![Page 43: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/43.jpg)
Formula Numbers
are found in mathematics and physics equations and formulas
![Page 44: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/44.jpg)
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
![Page 45: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/45.jpg)
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 numbersd=2r C=2πr T=2π√ (l/g)
Eff%=Wout/WinX 100
![Page 46: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/46.jpg)
Weakest Link Rule for Multiplying and Dividing Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the area of the rectangular deck.
![Page 47: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/47.jpg)
Weakest Link Rule for Multiplying and Dividing Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the area of the rectangular deck
A=L X W
![Page 48: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/48.jpg)
Weakest Link Rule for Multiplying and Dividing Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the area of the rectangular deck
A=L X W =(2.148m)(3.09m)
![Page 49: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/49.jpg)
Weakest Link Rule for Multiplying and Dividing Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the area of the rectangular deck
A=L X W =(2.148m)(3.09m) =6.63732 m2
![Page 50: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/50.jpg)
Weakest Link Rule for Multiplying and Dividing Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the area of the rectangular deck
A=L X W =(2.148m)(3.09m) =6.63732 m2 = =6.64 m2
![Page 51: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/51.jpg)
Weakest Link Rule for Multiplying and Dividing Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the area of the rectangular deck
A=L X W =(2.148m)(3.09m) =6.63732 m2 = =6.64 m2
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.
![Page 52: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/52.jpg)
Weakest Link Rule for Adding and Subtracting Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the perimeter of the rectangular deck
![Page 53: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/53.jpg)
Weakest Link Rule for Adding and Subtracting Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the perimeter of the rectangular deck
P = 2(L + W)
![Page 54: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/54.jpg)
Weakest Link Rule for Adding and Subtracting Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the perimeter of the rectangular deck
P = 2(L + W) = 2(2.148 m +3.09 m)
![Page 55: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/55.jpg)
Weakest Link Rule for Adding and Subtracting Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the perimeter of the rectangular deck
P = 2(L + W) = 2(2.148 m +3.09 m) = 2(5.238 m )
![Page 56: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/56.jpg)
Weakest Link Rule for Adding and Subtracting Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the perimeter of the rectangular deck
P = 2(L + W) = 2(2.148 m +3.09 m) = 2(5.238 m ) = 2(5.24 m)
![Page 57: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/57.jpg)
Weakest Link Rule for Adding and Subtracting Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the perimeter of the rectangular deck
P = 2(L + W) = 2(2.148 m +3.09 m) = 2(5.238 m ) = 2(5.24 m) =10.5 m
![Page 58: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/58.jpg)
Weakest Link Rule for Adding and Subtracting Measured Quantities
Example: A rectangular deck is 2.148 m long and 3.09 m wide. Find the perimeter of the rectangular deck
P = 2(L + W) = 2(2.148 m +3.09 m) = 2(5.238 m ) = 2(5.24 m) =10.5 mRule: When adding or subtracting, round the final
answer to the same number of decimal places as the least precise measured quantity in the calculation.
![Page 59: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/59.jpg)
☺Review Question
Two spheres touching each other have radii given by symbols r1 = 3.06 mm and r2 = 4.21 cm. Each sphere has a mass m1= 15.2 g and m2 = 4.1 kg.
a) If d = r1 + r2 , find d in meters
b)The constant G = 6.67 X 10-11 and the force of gravity between the spheres in Newtons is given by F = Gm1m2/d
2 . Given that all measured quantities must be in MKS units, find F in Newtons.
![Page 60: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/60.jpg)
☺Review Question
Two spheres touching each other have radii given by symbols r1 = 3.06 mm and r2 = 4.21 cm. Each sphere has a mass m1= 15.2 g and m2 = 4.1 kg.
a) If d = r1 + r2 , find d in meters
= 3.06 mm + 4.21 cm = 3.06 X 10-3 m + 4.21 X 10-2 m = 4.516 X 10-2 m = 4.52 X 10-2 m
![Page 61: Measurement and Significant Digits. >>>>>>>>>>>>>>>>>>>>> object ---------|---------|---------|---------| cm ruler 10 11 12 13 How do we record the length.](https://reader035.fdocuments.net/reader035/viewer/2022062219/5a4d1b297f8b9ab059998858/html5/thumbnails/61.jpg)
☺Review Question
b) The constant G = 6.67 X 10-11 and the force of gravity between the spheres in Newtons is given by F = Gm1m2/d
2 . Given that all measured quantities must be in MKS units, find F in Newtons.
F = Gm1m2/d2
= (6.67 X 10-11)(15.2 g)(4.1 kg)/(4.52 X 10-2 m)2
= (6.67 X 10-11)(15.2 x 10-3 kg)(4.1 kg)/(4.52 X 10-2 m)2
= 2.0345876 X 10-9 N = 2.0 X 10-9 N