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

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) -># #2color(white)(.) color(red)("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 color(white)(.)color(blue)("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")))#