# What are the significant figures rules?

1. Non-zero digits are always significant.
2. Leading zeros are never significant.
3. Internal zeros are always significant.
4. Trailing zeros may or may not be significant.

If there are any trailing zeros after the decimal point, they (all of the trailing zeros) are significant, but if they are all before the decimal point, then you can’t tell (different conventions are sometimes used in this case).

Examples:

0000343
(Not a common way to express a number, but the zeros are not significant.)

0.000343
Standard notation; still not significant

Internal Zeros:
3.404
304
30.04
All zeros are significant

Trailing Zeros:
3.400
3400.00
All zeros are significant

340
This is the ambiguous case. Sometimes the convention is used that if a decimal is shown, the zeros are all counted as significant:
340.
But that is just a convention, and may not always apply.

To remove the ambiguity, the number really should be expressed in , where all zeros (the x10 factor doesn’t count) are significant.
##3.4 xx10^2##
##3.40 xx10^2##

Note: when a number is expressed in scientific notation, there is one non-zero digit, followed by the decimal, followed by other digits, so there are never any leading zeros, and all zeros come after the decimal point, so they are always counted significant.

For further help, please see my video:

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