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125.340006 has seven significant figures if the resolution is to 0.0001: 1, 2, 5, 3, 4, 0, and 0. Zeros to the left of the first non-zero digit ( leading zeros ) are not significant . If a length measurement gives 0.052 km, then 0.052 km = 52 m so 5 and 2 are only significant; the leading zeros appear or disappear, depending on which unit is ...
3.01 × 10 8: 3 significant figures ... if there is a choice between numbers with the least significant digit 0 or 1, 4 or 5, 5 or 6, 9 or 0, then the digit different ...
In this formalism, the identities 1 = 0.999... and 1 = 1.000... reflect, respectively, the fact that 1 lies in both [0, 1]. and [1, 2], so one can choose either subinterval when finding its digits. To ensure that this notation does not abuse the "=" sign, one needs a way to reconstruct a unique real number for each decimal.
The above is not limited to subtractions, try = 1 + 1.405*2^(-48) in one cell, Excel rounds the display to 1,00000000000000000000, and = 0.9 + 225179982494413×2^(-51) in another, same display [d] above, different rounding for value and display, violates one of the elementary requirements in Goldberg (1991) [8] who states:
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0.08%. 0.07%. Up 1 basis point. ... with economic data indicating a continued decline from a peak of 9.1% in June 2022 to rates ... Economists view these figures as suggesting that inflation ...
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Thus 1 230 400 would become 1.2304 × 10 6 if it had five significant digits. If the number were known to six or seven significant figures, it would be shown as 1.230 40 × 10 6 or 1.230 400 × 10 6. Thus, an additional advantage of scientific notation is that the number of significant figures is unambiguous.