Significant figures意思
"Significant figures" or "significant digits" refer to the digits in a number that carry meaning or significance regarding its precision and accuracy. These digits provide information about the reliability of a measurement or a numerical value.
When recording measurements or performing calculations, scientists and mathematicians use significant figures to indicate the reliability of the numbers. The significant figures in a number include all the digits that are known, plus a final digit that is estimated, or uncertain.
Here are some rules for determining significant figures:
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All non-zero digits are significant. For example, in the number 123.4, all four digits are significant.
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Zeroes between non-zero digits are significant. In the number 101.23, all five digits are significant because the zeroes between the 1 and the 2, and between the 2 and the 3 are not placeholders.
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Zeroes at the end of a number but to the right of a decimal point are significant. For example, in the number 12.300, all four digits are significant.
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Zeroes at the end of a number that are to the left of a decimal point are not significant unless they are preceded by a non-zero digit. For example, in the number 100, only the last digit is significant, but in the number 100.0, all four digits are significant.
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Leading zeroes in a number are not significant. For example, in the number 0.00123, only the last three digits are significant.
When performing mathematical operations, the rules for significant figures dictate how many digits in the answer can be considered reliable:
- Addition and Subtraction: The answer should have the same number of decimal places as the number with the fewest decimal places in the problem.
- Multiplication and Division: The answer should have the same number of significant figures as the number with the fewest significant figures in the problem.
Significant figures are important in scientific and engineering contexts because they help prevent misinterpretation of numerical data by indicating the precision of a measurement or calculation.