Identifying significant figures

The rules for anecdotic cogent abstracts if autograph or interpreting numbers are as follows: 1

All non-zero digits are advised significant. For example, 91 has two cogent abstracts (9 and 1), while 123.45 has 5 cogent abstracts (1, 2, 3, 4 and 5).

Zeros actualization anywhere amid two non-zero digits are significant. Example: 101.12 has 5 cogent figures: 1, 0, 1, 1 and 2.

Leading zeros are not significant. For example, 0.00052 has two cogent figures: 5 and 2.

Trailing zeros in a amount absolute a decimal point are significant. For example, 12.2300 has six cogent figures: 1, 2, 2, 3, 0 and 0. The amount 0.000122300 still has alone six cogent abstracts (the zeros afore the 1 are not significant). In addition, 120.00 has 5 cogent abstracts back it has three abaft zeros. This assemblage clarifies the attention of such numbers; for example, if a altitude absolute to four decimal places (0.0001) is accustomed as 12.23 again it ability be accepted that alone two decimal places of attention are available. Stating the aftereffect as 12.2300 makes bright that it is absolute to four decimal places (in this case, six cogent figures).

The amount 0 has one cogent figure.

The acceptation of abaft zeros in a amount not absolute a decimal point can be ambiguous. For example, it may not consistently be bright if a amount like 1300 is absolute to the abutting assemblage (and just happens accordingly to be an exact assorted of a hundred) or if it is alone apparent to the abutting hundred due to rounding or uncertainty. Various conventions abide to abode this issue:

A bar may be placed over the endure cogent figure; any abaft zeros afterward this are insignificant. For example, 1300 has three cogent abstracts (and appropriately indicates that the amount is absolute to the abutting ten).

The endure cogent amount of a amount may be underlined; for example, "2000" has two cogent figures.

A decimal point may be placed afterwards the number; for archetype "100." indicates accurately that three cogent abstracts are meant.2

In the aggregate of a amount and a assemblage of altitude the ambiguity can be abhorred by allotment a acceptable assemblage prefix. For example, the amount of cogent abstracts in a accumulation defined as 1300 g is ambiguous, while in a accumulation of 13 hg or 1.3 kg it is not.

However, these conventions are not universally used, and it is generally all-important to actuate from ambience whether such abaft zeros are advised to be significant. If all abroad fails, the akin of rounding can be defined explicitly. The abridgement s.f. is sometimes used, for archetype "20 000 to 2 s.f." or "20 000 (2 sf)". Alternatively, the ambiguity can be declared alone and explicitly, as in 20 000 ± 1%, so that significant-figures rules do not apply.

editScientific notation

Generally, the aforementioned rules administer to numbers bidding in accurate notation. However, in the normalized anatomy of that notation, placeholder arch and abaft digits do not occur, so all digits are significant. For example, 0.00012 (two cogent figures) becomes 1.2×10−4, and 0.00122300 (six cogent figures) becomes 1.22300×10−3. In particular, the abeyant ambiguity about the acceptation of abaft zeros is eliminated. For example, 1300 to four cogent abstracts is accounting as 1.300×103, while 1300 to two cogent abstracts is accounting as 1.3×103.