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sigNificant fiGures!
- Thread starter hassam
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The rules for identifying significant digits when writing or interpreting numbers are as follows:
All non-zero digits are considered significant. For example, 91 has two significant figures (9 and 1), while 123.45 has five significant figures (1, 2, 3, 4 and 5).
Zeros appearing anywhere between two non-zero digits are significant. Example: 101.12 has five significant figures: 1, 0, 1, 1 and 2.
Leading zeros are not significant. For example, 0.00052 has two significant figures: 5 and 2.
Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has only six significant figures (the zeros before the 1 are not significant). In addition, 120.00 has five significant figures. This convention clarifies the precision of such numbers; for example, if a result accurate to four decimal places is given as 12.23 then it might be understood that only two decimal places of accuracy are available. Stating the result as 12.2300 makes clear that it is accurate to four decimal places.
The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is accurate to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty. Various conventions exist to address this issue:
A bar may be placed over the last significant digit; any trailing zeros following this are insignificant. For example, has three significant figures (and hence indicates that the number is accurate to the nearest ten).
The last significant figure of a number may be underlined; for example, "20000" has two significant figures.
A decimal point may be placed after the number; for example "100." indicates specifically that three significant figures are meant.[1]
However, these conventions are not universally used, and it is often necessary to determine from context whether such trailing zeros are intended to be significant. If all else fails, the level of rounding can be specified explicitly. The abbreviation s.f. is sometimes used, for example "20 000 to 2 s.f." or "20 000 (2 sf)". Alternatively, the uncertainty can be stated separately and explicitly, as in 20 000 ± 1%, so that significant-figures rules do not apply.
All non-zero digits are considered significant. For example, 91 has two significant figures (9 and 1), while 123.45 has five significant figures (1, 2, 3, 4 and 5).
Zeros appearing anywhere between two non-zero digits are significant. Example: 101.12 has five significant figures: 1, 0, 1, 1 and 2.
Leading zeros are not significant. For example, 0.00052 has two significant figures: 5 and 2.
Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has only six significant figures (the zeros before the 1 are not significant). In addition, 120.00 has five significant figures. This convention clarifies the precision of such numbers; for example, if a result accurate to four decimal places is given as 12.23 then it might be understood that only two decimal places of accuracy are available. Stating the result as 12.2300 makes clear that it is accurate to four decimal places.
The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is accurate to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty. Various conventions exist to address this issue:
A bar may be placed over the last significant digit; any trailing zeros following this are insignificant. For example, has three significant figures (and hence indicates that the number is accurate to the nearest ten).
The last significant figure of a number may be underlined; for example, "20000" has two significant figures.
A decimal point may be placed after the number; for example "100." indicates specifically that three significant figures are meant.[1]
However, these conventions are not universally used, and it is often necessary to determine from context whether such trailing zeros are intended to be significant. If all else fails, the level of rounding can be specified explicitly. The abbreviation s.f. is sometimes used, for example "20 000 to 2 s.f." or "20 000 (2 sf)". Alternatively, the uncertainty can be stated separately and explicitly, as in 20 000 ± 1%, so that significant-figures rules do not apply.