How many times have you said to yourself, "I hate significant figures!"  Although many chemistry students would agree that significant figures are the bane of their existence,  we'll be using sig figs throughout the year.   Learn the rules well and use them consistently!

Refer back to this page if you  need clarification or additional examples for the significant figure rules.

Rule 1.  All nonzero digits are significant.             

• 45 has 2 sig figs.
• 123 has 3 sig figs.
• 59245 has 5 sig figs.

Rule 2.  "Captive" zeros are always significant.

• 101 has 3 sig figs.
• 2005 has 4 sig figs.

Rule 3.  "Leading" zeros are never significant.

• 0.0037 has 2 sig figs.
• 0.000409 has 3 sig figs.
• 0.000000000008231 has 4 sig figs.

Rule 4.  "Trailing" zeros are not significant UNLESS there is a decimal point in the  number.

• 40  has 1 sig fig.
• 40. has 2 sig figs.
• 40.0 has three sig figs.
• 3000 has 1 sig fig.
• 3000.0 has 5 sig figs.
• 0.003080 has 4 sig figs.  (Rules 1, 2, 3, and 4!)

Sometimes, significant zeroes are indicated by placing a bar over the last significant zero in the number.  For example, 30400 would have four significant figures; the last zero is not significant.

Rule 5.  Digits written out in scientific notation are significant. 

• 1 x 10^-7 has 1 sig fig.
• 2.0 x 10⁴ has 2 sig figs.
• 6.02 x 10²³ has 3 sig figs.

Rule 6.  All measured values are significant.  To indicate precision, measured values should be recorded one decimal place beyond the smallest division marked on the measuring tool.

• A 100 mL graduated cylinder is marked to 1 mL divisions.  All volume readings should be recorded to 0.1 mL.

When adding and subtracting with significant figures, the answer should be rounded so that it has no more decimal places than the value with fewest decimal places.

• If you need to find the sum of 12.2 cm and 3.042 cm, your answer must be rounded to one decimal place, because 12.2 cm is recorded to only one decimal place.  The correct answer is 15.2 cm.

When  multiplying and dividing with significant figures, the answer should be rounded so that it has no more significant figures than the value with the fewest significant figures.

• If you need to find the product of 12.2 cm and 3.042 cm, your answer must be rounded to three significant figures.  12.2 cm has three sig figs, compared to 4 sig figs for 3.042 cm, so you are only allowed three sig figs in your answer.  The correct answer would be 37.1 cm².