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phy131studiof15:lectures:chapter1 [2015/08/24 08:49] mdawber [Stating errors] |
phy131studiof15:lectures:chapter1 [2015/08/24 09:19] (current) mdawber [Scientific Notation] |
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Examples: | Examples: | ||

- | $0.000056$ m = $5.6 \times 10^{-5}$ m or $5.6 \times 10^{-2}$ mm. | + | $0.000056$m = $5.6 \times 10^{-5}$m or $5.6 \times 10^{-2}$mm. |

- | $795,000$ g = $7.95 \times 10^{5}$ g or $7.95 \times 10^{2}$ kg or $795$ kg. | + | $795,000$g = $7.95 \times 10^{5}$g or $7.95 \times 10^{2}$kg or $795$kg. |

In general it is not correct to give more significant figures for a number than the precision to which you know it. However you should not round off numbers too early in a calculation, as this can affect the accuracy of the final answer. | In general it is not correct to give more significant figures for a number than the precision to which you know it. However you should not round off numbers too early in a calculation, as this can affect the accuracy of the final answer. | ||

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{{http://ic.sunysb.edu/Class/phy133s/vidspics/bullsyefourframesd.png}} | {{http://ic.sunysb.edu/Class/phy133s/vidspics/bullsyefourframesd.png}} | ||

- | Think of the round object as an archery target. The archer shoots some number of arrows at it, and each dot shows where one landed. Now think of the "bull's eye" -- the larger black dot in the center -- as the "true" value of some quantity that's being measured, and think of each arrow-dot as a measurement of that quantity. The problem is that the one doing the measurements does not know the "true" value of the quantity; s/he's trying to determine it experimentally, and this means there must be uncertainty associated with the experimentally determined value. Note that each archery target -- we'll call them 1,2,3,4 from left to right -- shows a different distribution of arrow-hit/measurements. | + | Think of the round object as an archery target. The archer shoots some number of arrows at it, and each dot shows where one landed. Now think of the "bull's eye" -- the larger black dot in the center -- as the "true" value of some quantity that's being measured, and think of each arrow-dot as a measurement of that quantity. The problem is that the one doing the measurements does not know the "true" value of the quantity; they are trying to determine it experimentally, and this means there must be uncertainty associated with the experimentally determined value. Each archery target shows a different distribution of arrow-hit/measurements. |