# How do you round 1,566,311 into 3 significant figures?

Feb 28, 2017

$1 , 570 , 000$

#### Explanation:

So, you know that you must round this number

$1 , 566 , 311$

to $3$ significant figures. The first thing to do here is to start at the first figure of the number and count $3$ figures as you move toward the last figure of the number.

In your case, you should end up on $\textcolor{red}{6}$, since

$\stackrel{\textcolor{b l u e}{1}}{1} , \stackrel{\textcolor{b l u e}{2}}{5} \stackrel{\textcolor{b l u e}{3}}{\textcolor{red}{6}} 6 , 311$

Now, the trick here is to look at the figure that follows the $\textcolor{red}{6}$ and compare it to $5$. If this figure is greater than or equal to $5$, you will round up. On the other hand, if this figure is smaller than $5$, you will round down.

"for a certain figure: " {("if" >= 5 -> "round up"), ("if" < 5 -> "round down") :}

In this case, the figure that follows $\textcolor{red}{6}$ is $\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{6}$.

$\stackrel{\textcolor{b l u e}{1}}{1} , \stackrel{\textcolor{b l u e}{2}}{5} \stackrel{\textcolor{b l u e}{3}}{\textcolor{red}{6}} \textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{6} , 311$

Since

$\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{6} \ge 5$

you will have to round up by adding $1$ to the value of $\textcolor{red}{6}$.

$\textcolor{red}{6} \text{ "stackrel(color(white)(acolor(darkgreen)("rounded up")aaa))(->) " } \textcolor{red}{7}$

To finish rounding up the initial number, replace all the figures that follow $\textcolor{red}{7}$ with $0$. You will have

$\stackrel{\textcolor{b l u e}{1}}{1} , \stackrel{\textcolor{b l u e}{2}}{5} \stackrel{\textcolor{b l u e}{3}}{\textcolor{red}{6}} \textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{6} , 311 \text{ "stackrel(color(white)(acolor(purple)("rounded to 3 sig figs")aaa))(->)" } \stackrel{\textcolor{b l u e}{1}}{1} , \stackrel{\textcolor{b l u e}{2}}{5} \stackrel{\textcolor{b l u e}{3}}{\textcolor{red}{7}} 0 , 000$