Question

When I round 6396 to 3 significant figures, I get 6400. I was double checking my work and used scientific notation for 6400, which is 6.4*10³, but when I counted the significant figures in scientific notation, I only get 2, which are 6 and 4, but there were supposed to be 3. Anyone can help to explain?

Answer 1

This is one slight annoyance when it comes to sig figs, in my opinion anyway. You did the steps correctly. The 639 bumps up to 640, so 6396 rounds to 6400 when rounding to 3 sig figs.

Normally the trailing zeros, ie zeros on the right, are not significant. So 6400 shows only 2 sig figs. What we need to do is draw a horizontal line over the first zero to show that it is significant (while the other zero is not significant)

So you'll write it like this

This notation can be problematic when it comes to decimals because it could be easily mixed up with the repeating decimal notation.

When you convert to scientific notation, you would get .

In short:

Here the zero is significant because the zero is present in the scientific notation result. Writing shows 2 sig figs while has 3 sig figs.

It's similar to how the number has 2 sig figs while has 3 sig figs. While the zero is trailing, having it after a decimal point indicates to the reader that you achieved this level of accuracy.

Answer 2

This is one slight annoyance when it comes to sig figs, in my opinion anyway. You did the steps correct. The 639 bumps up to 640, so 6396 rounds to 6400 when rounding to 3 sig figs.

Normally the trailing zeros, ie zeros on the right, are not significant. So 6400 shows only 2 sig figs. What we need to do is draw a horizontal line over the first zero to show that it is significant (while the other zero is not significant)

So you'll write it like this
`64\overline{0}0`

This notation can be problematic when it comes to decimals because it could be easily mixed up with the repeating decimal notation.

When you convert
`64\overline{0}0` to scientific notation, you would get
`6.40 * 10^3`.

In short:
`64\overline{0}0 = 6.40 * 10^3`

Here the zero is significant because the zero is present in the scientific notation result. Writing
`6.4 * 10^3` shows 2 sig figs while
`6.40 * 10^3` has 3 sig figs.

It's similar to how the number
`5.7` has 2 sig figs while
`5.70` has 3 sig figs. While the zero is trailing, having it after a decimal point indicates to the reader that you achieved this level of accuracy.