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0.00034 has 2 significant figures (3 and 4) if the resolution is 0.00001. Zeros to the right of the last non-zero digit (trailing zeros) in a number with the decimal point are significant if they are within the measurement or reporting resolution. 1.200 has four significant figures (1, 2, 0, and 0) if they are allowed by the measurement resolution.
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 ...
All of the significant digits remain, but the placeholding zeroes are no longer required. 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 ...
E.g. decimal 0.1 has the IEEE double representation 0 (1).1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 1010 × 2^(-4); when added to 140737488355328.0 (which is 2 +47) it will lose all of its bits, except the first two. Thus from '= ( 140737488355328.0 + 0.1 - 140737488355328.0) it will come back as 0.09375 instead of 0.1 when ...
The standard definition of the number 0.999... is the limit of the sequence 0.9, 0.99, 0.999, ... . A different definition involves an ultralimit, i.e., the equivalence class [(0.9, 0.99, 0.999, ...)] of this sequence in the ultrapower construction, which is a number that falls short of 1 by an infinitesimal amount. [66]
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