Question

What is $1.283333... rounded to the nearest cent?

Answer 1

`$1.28`

Explanation:

A cent is a hundredth of a dollar. So we round to the nearest hundredth.
The hundredths digit is `8`. The digit after it is `3`. `3` is less than `5`, so we don't change `8`. Therefore, the answer is `$1.28`.

Answer 2

$1.28

Explanation:

I'm going to assume we're using Dollars and Cents for this question.

We have an amount: $1.283333... how much is this, rounded to the nearest cent.

We can look at this question by seeing the different positions the numbers hold:

`$overbrace(1)^(100 " cents")"."overbrace(2)^(10" cents")color(white)(0)overbrace(8)^(1" cent")color(white)(0)overbrace(3)^(1/10" cent")`

When we round, we look at the position we are rounding to - in this case, the closest cent.

`$overbrace(1)^(100 " cents")"."overbrace(2)^(10" cents")color(white)(0)overbrace(color(red)8)^(color(red)(1" cent"))color(white)(0)overbrace(3)^(1/10" cent")`

What are the possible answers? We could have our number be

$1.28

or since we're on our way to the next highest cent, it could also be

$1.29

Which one is right? To answer that, we look to the next position down and see if we're halfway (or more) to the next highest cent yet:

`$overbrace(1)^(100 " cents")"."overbrace(2)^(10" cents")color(white)(0)overbrace(color(red)8)^(color(red)(1" cent"))color(white)(0)overbrace(color(blue)(3))^(color(blue)(1/10" cent"))`

If the blue number is 0, 1, 2, 3, or 4, we aren't halfway or more to the next highest red number, and so the red number stays put. In this case, we'd get $1.28.

If the blue number is 5, 6, 7, 8, or 9, then we are more than halfway to the next number and so the red number rounds up by 1. We'd get $1.29.

In our question, the blue number is 3, which means the red number stays put. We get $1.28.