Question

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

Answer 1

`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 `color(red)(6)`, since

`stackrel(color(blue)(1))(1), stackrel(color(blue)(2))(5) stackrel(color(blue)(3))(color(red)(6))6,311`

Now, the trick here is to look at the figure that follows the `color(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 `color(red)(6)` is `color(darkorange)(6)`.

`stackrel(color(blue)(1))(1), stackrel(color(blue)(2))(5) stackrel(color(blue)(3))(color(red)(6))color(darkorange)(6),311`

Since

`color(darkorange)(6) >= 5`

you will have to round up by adding `1` to the value of `color(red)(6)`.

`color(red)(6) " "stackrel(color(white)(acolor(darkgreen)("rounded up")aaa))(->) " "color(red)(7)`

To finish rounding up the initial number, replace all the figures that follow `color(red)(7)` with `0`. You will have

`stackrel(color(blue)(1))(1), stackrel(color(blue)(2))(5) stackrel(color(blue)(3))(color(red)(6))color(darkorange)(6),311 " "stackrel(color(white)(acolor(purple)("rounded to 3 sig figs")aaa))(->)" " stackrel(color(blue)(1))(1), stackrel(color(blue)(2))(5) stackrel(color(blue)(3))(color(red)(7))0,000`