How many significant figures are there in the measurement 100.0001 kg?

Feb 21, 2017

$7$

Explanation:

For starters, you should know that all non-zero digits are significant, so right from the start, you can say that the measurement has at least $2$ significant figures

color(black)(color(red)(1)00.000color(red)(1) -> $2 \textcolor{w h i t e}{.} \textcolor{red}{\text{non-zero")color(white)(.)color(black)("digits}}$

Now, the more interesting thing to determine is how many zeroes, if any, are significant.

As it turns out, any and all zeros that follow a non-zero digit and are followed by a non-zero digit are significant. In other words, these zeros are significant because they are sandwiched between two non-zero digits.

In your case, you can say that the measurement has $5$ sandwiched zeros

color(black)(1color(blue)(00.000)1 -> $5 \textcolor{w h i t e}{.} \textcolor{b l u e}{\text{sandwiched zeros}}$

Therefore, you can say that your measurement has $7$ significant figures

color(red)(1)color(blue)(00.000)color(red)(1) -> {(color(red)(2)color(white)(.)"non-zero digits"), (color(blue)(5)color(white)(.)"sandwiched zeros") :} = color(darkgreen)(ul(color(black)("7 significant figures")))