# Question a89be

Aug 16, 2017

$8$

#### 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.

$\textcolor{b l a c k}{\textcolor{red}{1} 0 \textcolor{red}{9} 0.00 \textcolor{red}{1} 0} \to \text{ 3 non-zero digits: } \left\{\textcolor{red}{1} , \textcolor{red}{9} , \textcolor{red}{1}\right\}$

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 $\textcolor{red}{1}$ and is followed by $\textcolor{red}{9}$

$\textcolor{b l a c k}{\textcolor{red}{1} \textcolor{b l u e}{0} \textcolor{red}{9} 0.00 \textcolor{red}{1} 0}$

The second, third, and fourth sandwiched zeros follow $\textcolor{red}{9}$ and are followed by $\textcolor{red}{1}$. This means that your number contains

$\textcolor{b l a c k}{\textcolor{red}{1} \textcolor{b l u e}{0} \textcolor{red}{9} \textcolor{b l u e}{0} . \textcolor{b l u e}{00} \textcolor{red}{1} 0} \to \text{ 4 sandwiched zeros: } \left\{\textcolor{b l u e}{0} , \textcolor{b l u e}{0} , \textcolor{b l u e}{0} , \textcolor{b l u e}{0}\right\}$

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 $\textcolor{red}{1}$ that's in the thousandths place

$\textcolor{b l a c k}{\textcolor{red}{1} \textcolor{b l u e}{0} \textcolor{red}{9} \textcolor{b l u e}{0} . \textcolor{b l u e}{00} \textcolor{red}{1} \textcolor{g r e e n}{0}} \to \text{ 1 significant trailing zero: } \left\{\textcolor{g r e e n}{0}\right\}$

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

color(white)(aaaaaaa)color(red)("3 non-zero digits") " "+#
$\textcolor{w h i t e}{a a a a a} \textcolor{b l u e}{\text{4 sandwiched zeros}}$
$\textcolor{g r e e n}{\text{1 significant trailing zero}}$
$\frac{\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a a a}}{\textcolor{w h i t e}{a}}$
$\textcolor{w h i t e}{a a a a a} \text{8 significant figures}$