Most significant digit
| Fit approximation | |
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| Concepts | |
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Orders of approximation Scale analysis · Big O notation Curve fitting · False precision Significant figures |
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| Other fundamentals | |
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Approximation · Generalization error Taylor polynomial Scientific modelling |
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The significant figures of a number are digits that carry meaning contributing to its measurement resolution. This includes all digits except:
Significance arithmetic are approximate rules for roughly maintaining significance throughout a computation. The more sophisticated scientific rules are known as propagation of uncertainty.
Numbers are often rounded to avoid reporting insignificant figures. For example, it would create false precision to express a measurement as 12.34500 kg (which has seven significant figures) if the scales only measured to the nearest gram and gave a reading of 12.345 kg (which has five significant figures). Numbers can also be rounded merely for simplicity rather than to indicate a given precision of measurement, for example, to make them faster to pronounce in news broadcasts.
Specifically, the rules for identifying significant figures when writing or interpreting numbers are as follows:
In most cases, the same rules apply to numbers expressed in scientific notation. However, in the normalized form of that notation, placeholder leading and trailing digits do not occur, so all digits are significant. For example, 0.00012 (two significant figures) becomes 1.2×10−4, and 0.00122300 (six significant figures) becomes 1.22300×10−3. In particular, the potential ambiguity about the significance of trailing zeros is eliminated. For example, 1300 to four significant figures is written as 1.300×103, while 1300 to two significant figures is written as 1.3×103.
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