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Measurement and Uncertainty (测量及其误差)
Experiments and therefore measurements play an essential role in physics. Accurate measurement are undoubtedly important, but no measurement is absolutely precise. There is always an uncertainty associated with every measure -ment.
(accuracy and precision, P3)
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Significant Figures
(有效数字) In general, a significant figure in a measurement is a reliably known digit. You SHOULD avoid the temptation to keep more digits in the final answer than is justified. When multiplying several quantities, the number of significant figures in the final answer is the same as the number of significant figures in the quantity having the lowest number of significant figures. The same rule applies to division. When numbers are added or subtracted, the number of decimal places in the result should equal to the smallest number of decimal places of any term in the sum. the number of decimal places 小数点后的位数
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However, to obtain the most accurate result, you should normally keep an extra significant figure or two throughout a calculation, and round off only in the final result.
General rule for rounding off numbers: the last digit retained is to be increased by 1 if the last digit dropped is greater than 5. If the last digit dropped is less than 5, the last digit retained remains unchanged. If the last digit dropped is equal to 5, the remaining digit should be rounded to the nearest even number.
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Scientific Notion
Numbers are commonly written in "powers of ten", or "scientific notion".
0.0030 = 3.0 ×10 , 34500=3.45 × 10
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One advantage of scientific notion is that it allows the number of significant figures to be clearly expressed.
E.g., 36900 can be expressed as 3.69 × 104 or 3.690 × 104 ,
but the latter has one more significant figure.
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Standards of Length, Mass, and Time
(SI system, Système International)
Length, meter (长度,米)

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