Today we will be discussing the four rules of determining the number of significant figures a number has, as well as how to add, subtract, multiply, and divide sig figs! But first, what are sig figs? The significant figures of a number are digits that carry meaning contributing to its measurement resolution.
The significant figures of a number are digits that carry meaning contributing to its measurement resolution.
EXAMPLE: 5.6 (2)
All non zero digits are significant.
RULE NUMBER ONE
The first rule is that all non zero digits are significant. For example, 5.6 has two sig figs because both are non zero digits.
The second rule is that all zeros sandwiched between two significant figures are themselves significant. For example, the zero is 105 is significant because it is sandwiched between two non zero digits.
EXAMPLE: 105 (3)
RULE NUMBER TWO
All zeros sandwiched in between two significant figures are themselves significant.
RULE NUMBER THREE
Zeros at the beginning of a number are never significant.
EXAMPLE: 0.0000056 (2)
The third rule is that zeros at the beginning of a number are never significant. For example, 0.0000056 only has two sig figs because the zeros come before the significant digits.
Rule number four is that trailing zeros are not significant unless there is a decimal present in the number. For example, 5600000 has two sig figs because the trailing zeros are not significant, but 345.560 has six sig figs because the last zero counts due to there being a decimal present.
RULE NUMBER FOUR
A. Trailing zeros are not significant EXAMPLE: 5600000 (2) B. Trailing zeros are significant if a zero is written in the number EXAMPLE: 345.560 (6)
Finally, there are two different sets of rules when it comes to determining sig figs when performing mathematical calculations. When addition or subtraction is performed, answers are rounded to the least significant decimal place as seen in the example. When multiplication or division is performed, answers are rounded to the number of digits that corresponds to the fewest number of sig figs in any of the numbers used in the calculation, as seen in the example.
DETERMINING SIG FIGS WHEN PERFORMING MATHEMATICAL CALCULATIONS