​9560 has 3 significant figures

​The non-zeros all count 9, 5, 6

​

​The last zero does not count. It is a trailing zero, which can sometimes count, but NOT if there isn't a decimal point.

​

​(see next question for an example when a decimal point is present)

​9560.0 has 5 significant figures

​The non-zeros all count 9, 5, 6

​

​The zeros also count. They are trailing zeros, meaning they come after the last non-zero digit (when reading left-to-right), AND THERE IS a decimal point.

​

​Trailing zeros count if a decimal point is present. That's one of our rules

The No, Yes, Maybe rules of zeros approach

​No - Leading zeros NEVER count (these are zeros that lead to the first non-zero) 0.0035 has 3 leading zeros... none of them count as significant

Yes - captive zeros Always count (these are zeros between non-zeros) 305 has 1 captive zero... counts! 706704 has 2 captive zeros, they count

​Maybe - trailing zeros might count. They DO COUNT if there is a decimal place present. (otherwise no) In 55700 , the 2 trailing zeros would NOT count because there is no decimal point present.

A slight variation... 55700.0 would now mean the trailing zeros DO count

​THEN, JUST REMEMBER THAT ALL NON-ZEROS COUNT

​See this online textbook section for a more detailed explanation of the YES, NO, Maybe approach (additional examples)

​OPENSTAX 1.5 Measurement Uncertainty, Accuracy, and Precision

https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision ​

Let's Check Comprehension​

a few example problems​

54010 cm has 4 significant figures

All non-zeros count

the captive zero counts

BUT, the trailing zero does not count. (no decimal point in the number)​

540.10 cm has 5 significant figures

All non-zeros count

the captive zero counts

The trailing zero does count. (decimal point in the number)​

0.054010 cm has 5 significant figures

All non-zeros count

the leading zeros do NOT count​

the captive zero counts

The trailing zero does count. (decimal point in the number)​

Sig Fig rounding after Multiplication or Division

For multiplication and division use the weakest link rule: 

​

Scan your calculation for the value with the LEAST number of significant figures. This number determines the number of significant figures allowed in the answer.

​

85.0 cm x 14 cm = ? cm² answer should have 2 significant figures since 14 cm has the least and it has 2.

​

85.0 cm x 14 cm = 1190 cm² , but must round! answer is 1200 cm² based on needing to limit it to having 2 sig figs. NOTICE that I now have a placeholder zero in the tens spot and my answer still goes to the thousands spot. I didn't truncate my number, I only rounded it.

In calculation 3.11 x 2.1 , value of 2.1 has the least number of significant figures.

​

It has 2 sig figs. Thus, your final answer just be rounded to have 2 sig figs.​

​

95.07 g / 23.0 cm³ = 4.133478261 g/cm³​

​However, answer must be rounded to have 3 significant figures since 23.0 only has 3 sig figs.

​

​4.13 g/cm³ is how it should be reported.

​The End. Did you...

• ​gain confidence identifying the number of significant figures in a given value?

• ​understand how to round an answer based on significant figures in the values within its calculation? (for multiplication or division