Editing Scientific notation (section)

== Significant figures ==
{{Main|Significant figures}}
A significant figure is a digit in a number that adds to its precision. This includes all nonzero numbers, zeroes between significant digits, and zeroes [[significant figures#Identifying significant digits|indicated to be significant]]. Leading and trailing zeroes are not significant digits, because they exist only to show the scale of the number. Unfortunately, this leads to ambiguity. The number {{val|1230400}} is usually read to have five significant figures: 1, 2, 3, 0, and 4, the final two zeroes serving only as placeholders and adding no precision. The same number, however, would be used if the last two digits were also measured precisely and found to equal 0 – seven significant figures.

When a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the placeholding zeroes are no longer required. Thus {{val|1230400}} would become {{val|1.2304E6}} if it had five significant digits. If the number were known to six or seven significant figures, it would be shown as {{val|1.23040E6}} or {{val|1.230400E6}}. Thus, an additional advantage of scientific notation is that the number of significant figures is unambiguous.

=== Estimated final digits ===
It is customary in scientific measurement to record all the definitely known digits from the measurement and to estimate at least one additional digit if there is any information at all available on its value. The resulting number contains more information than it would without the extra digit, which may be considered a significant digit because it conveys some information leading to greater precision in measurements and in aggregations of measurements (adding them or multiplying them together).

Additional information about precision can be conveyed through additional notation. It is often useful to know how exact the final digit or digits are. For instance, the accepted value of the mass of the [[proton]] can properly be expressed as {{val|1.67262192369E-27|(51)|u=kg}}, which is shorthand for {{val|1.67262192369E-27|0.00000000051|u=kg}}. However it is still unclear whether the error ({{val|5.1E-37}} in this case) is the maximum possible error, [[standard error]], or some other [[confidence interval]].