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

1 Answer
Feb 28, 2017

Answer:

#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#