# Significant figures: Trailing Zeros in Scientific Notation.

I'm wondering how you determine the number of significant figures of a number in scientific notation with trailing zeros.

For example:

$3100.0*10^2$

(which is not in correct scientific notation) has how many significant figures?

On first guess you would say the number has 5 sigfigs because it has a decimal point, but in reality, that decimal point just helps indicate magnitude. All trailing zeroes can be removed and the number changed to

$3.1*10^5$

Now the number has only 2 significant figures.

Which answer is correct: 2 or 5? Can someone please clarify this

## 2 Answers

In your case, the number $3100.0 \cdot 10^2$ has five significant figures. When you write it as $\text{something} \cdot 10^5$, you need to keep the number of significant figures, so the correct way to write the number while preserving precision is $3.1000 \cdot 10^5$ and not $3.1 \cdot 10^5$.

There are 5. The 0 after the decimal point is there because it is significant, and intermediate zeroes are also significant.