How many significant figures are there in the number 1008500?

Aug 20, 2016

$5$ significant figures

Explanation:

The first thing to look for when deciding how many significant figures you have in a value is the number of non-zero digits it contains.

Non-zero digits are always significant, so right from the start you know that your number will contain at least as many significant figures as the number of non-zero digits it contains.

In this case, you have $1$, $8$, and $5$ as non-zero, and thus significant, digits.

Now, your number also contains two sandwiched zeros. By definition, a sandwiched zero is a zero that follows and is followed by at least one non-zero digit. Sandwiched zeros are always significant.

In your case, you have

$1 \textcolor{red}{00} 8500 \to$ two sandwiched zeros, significant

Here two zeros follow $1$, a non-zero digit, and are followed by $8$ and $5$, two non-zero digits

Finally, your number also contains two trailing zeros. Trailing zeros are zeros that follow at least one non-zero digit and are not followed by other non-zero digits.

When trailing zeros do not follow the decimal point, they are not significant. In your case, you have

$10085 \textcolor{p u r p \le}{00} \to$ two trailing zeros, NOT significant

Therefore, you can say that your number has $5$ significant figures

$1 \textcolor{red}{00} 85 \textcolor{p u r p \le}{00} \to \left\{\begin{matrix}3 \textcolor{w h i t e}{a} \text{non-zero digits & signifcant " color(green)(sqrt()) \\ color(red)(2)color(white)(a)"sandwiched zeros & significant "color(green)(sqrt()) \\ color(purple)(2)color(white)(a)"trailing zeros & NOT significant } \textcolor{red}{\times}\end{matrix}\right.$