Question #9f7af

The key here is the operation that you perform in order to get the answer.

In this particular case, you can get the volume of the aquarium by multiplying its length, its width, and its height, i.e. you can treat the aquarium as a rectangular prism.

#V_"aquarium" = "12.9 in" xx "7.67 in" xx "4.11 in"#

#V_"aquarium" = "406.65573 in"^3#

Now, the thing to remember about multiplication and division is that the result of these operations must always be rounded to the number of sig figs present in the measurement that has the least number of sig figs.

You have

• #"12.9 " -> " 3 non-zero digits = 3 sig figs"#
• #"7.67 " -> " 3 non-zero digits = 3 sig figs"#
• #"4.11 " -> " 3 non-zero digits = 3 sig figs"#

In your case, all three measurements have #3# sig figs, so you can say that their product must be rounded to #3# sig figs.

In order to round the answer to #3# sig figs, you must take a look at the #color(blue)("4th")# sig fig and compare it to #color(red)(5)#. If the #color(blue)("4th")# sig figs is #>= color(red)(5)#, then you must add #1# to the #color(blue)("3rd")# third sig fig and drop the rest of the figures and the decimal point.

If the #color(blue)("4th"# sig figs is #< color(red)(5)#, then you will leave the #color(blue)("3rd"# sig figs unchanged and drop the rest of the figures and the decimal point.

#stackrel(color(blue)(1))(4)stackrel(color(blue)(2))(0)stackrel(color(blue)(3))(6). stackrel(color(blue)(4))(6)5573#

In your case, you have

#6 >= color(red)(5) -># the #color(blue)("4th"# sig figs is greater than or equal to #color(red)(5)#

This means that you will add #1# to the #color(blue)("3rd"# sig fig

#6 + 1 = 7#

and drop the rest of the figures and the decimal point.

#stackrel(color(blue)(1))(4)stackrel(color(blue)(2))(0)stackrel(color(blue)(3))(7). color(red)(cancel(color(black)(65573)))#

This means that you have

#V_"aquarium" = "12.9 in" xx "7.67 in" xx "4.11 in" = "407 in"^3#

The answer is rounded to three sig figs.