# Question 15f43

Mar 17, 2017

$5$

#### Explanation:

The first thing to look for when trying to figure out how many significant figures you have in a measurement are non-zero digits.

Non-zero digits are always significant, regardless if they are added before or after the decimal place. In your case, you have three non-zero digits

color(black)(color(red)(7)0. color(red)(8)0color(red)(4) -> three non-zero digits

so you know for a fact that the measurement has at least three sig figs.

The first zero

$7 \textcolor{b l u e}{0} .804$

is significant because it follows a non-zero digit, i.e. $7$, and it is being followed by a non-zero digit, i.e. $8$. Zeros that are "sandwiched" between two non-zero digits are always significant.

Notice that the second zero

$70.8 \textcolor{b l u e}{0} 4$

is also sandwiched between two non-zero digits. This zero follows $8$ and it is being followed by $4$, so you know for a fact that this zero is significant.

Therefore, you can say that the measurement given to has $5$ significant figures

color(black)(color(red)(7)color(blue)(0). color(red)(8)color(blue)(0)color(red)(4) -> {("three non-zero digits"), ("two sandwiched zeros") :}#