# How many significant digits are contained in the number 1804.00?

Jul 30, 2016

$6$

#### Explanation:

The first thing to notice here is that your number contains three non-zero digits, $1$, $8$, and $4$. As you know, all non-zero digits are significant.

$\textcolor{b l u e}{18} 0 \textcolor{b l u e}{4} .00 \to$ $3 \textcolor{w h i t e}{a} \textcolor{b l u e}{\text{non-zero digits}}$

Next, notice that your number contains a sandwiched zero, which is a zero digit that follows and is followed by a non-zero digit. Sandwiched zeros are significant.

In your case, you have a zero that is sandwiched between $8$ and $4$, both non-zero digits.

$\textcolor{b l u e}{18} \textcolor{red}{0} \textcolor{b l u e}{4} .00 \to \left\{\left(3 \textcolor{w h i t e}{a} \textcolor{b l u e}{\text{non-zero digits")), (1color(white)(a)color(red)("sandwiched zero}}\right)\right.$

Finally, notice that your number also contains two trailing zeros. A trailing zero is zero that follows a decimal point or a non-zero digit and is not followed by a non-zero digit.

Trailing zeros that follow the decimal point are always significant.

$\textcolor{b l u e}{18} \textcolor{red}{0} \textcolor{b l u e}{4} . \textcolor{\mathrm{da} r k g r e e n}{00} \to \left\{\left(3 \textcolor{w h i t e}{a} \textcolor{b l u e}{\text{non-zero digits")), (1color(white)(a)color(red)("sandwiched zero")), (2color(white)(a)color(darkgreen)("trailing zeros}}\right)\right.$
$1804.00 \to 6$ significant figures.