Question #a89be

1 Answer
Aug 16, 2017

Answer:

#8#

Explanation:

For starters, you know that all non-zero digits are significant, so you can say that your number has at least #3# significant figures because it contains #3# non-zero digits.

#color(black)(color(red)(1)0color(red)(9)0.00color(red)(1)0) -> " 3 non-zero digits: " { color(red)(1), color(red)(9), color(red)(1) }#

Now, you should also know that all zeros that are sandwiched between two non-zero digits are significant. In other words, if a zero follows a non-zero digit and is followed by a non-zero digit, regardless if other zeros are adjacent, it is significant.

In your case, you have #4# sandwiched zeros. The first sandwiched zero follows #color(red)(1)# and is followed by #color(red)(9)#

#color(black)(color(red)(1)color(blue)(0)color(red)(9)0.00color(red)(1)0)#

The second, third, and fourth sandwiched zeros follow #color(red)(9)# and are followed by #color(red)(1)#. This means that your number contains

#color(black)(color(red)(1)color(blue)(0)color(red)(9)color(blue)(0). color(blue)(00)color(red)(1)0) -> " 4 sandwiched zeros: " {color(blue)(0), color(blue)(0), color(blue)(0), color(blue)(0) }#

Finally, you should know that trailing zeros, i.e. zeros that follow a non-zero digit and are not followed by a non-zero digit, that follow a decimal point are significant.

In this case, you have one trailing zero that follows the decimal point and the #color(red)(1)# that's in the thousandths place

#color(black)(color(red)(1)color(blue)(0)color(red)(9)color(blue)(0). color(blue)(00)color(red)(1)color(green)(0)) -> " 1 significant trailing zero: " {color(green)(0)}#

Therefore, you can say that your number has a total of

#color(white)(aaaaaaa)color(red)("3 non-zero digits") " "+#
#color(white)(aaaaa)color(blue)("4 sandwiched zeros")#
#color(green)("1 significant trailing zero")#
#color(white)(aaaaaaaaaaaaaaaaaaaaaa)/color(white)(a)#
#color(white)(aaaaa)"8 significant figures"#