What is 8243.88316 rounded to the nearest hundredth?

Question

Everly Taylor · Accepted Answer

8243.88 - look at the position we're rounding to and the one to the right to determine what to round to.

Let's examine the figure to get things started: 8243.88316 Okay, there are a lot of numbers there, most of which are unimportant to us. Let's rewrite the number so that we can concentrate on the two that we do care about: the digit to the right and the one in the hundredth position. XXXX.X83XX What does it mean that we should round this to the nearest hundredth? First, a little about rounding. If you were to divide the number of people at a party by the number of slices of pizza that were left, you would not come to the conclusion that each person could eat 0.53846154 slices; rather, you would conclude that each person could have half a slice and that one person would miss out. This is because we don't care about all those digits in 7 divided by 13. That is one reason why we round: to help reveal the things that we care about (like a half slice of pizza) and discard the things we don't (like 0.53846154). Because anything more would be meaningless detail, we are only interested in that number up to the hundredths position in our current question. We could just drop everything to the right of the hundredths position - the 316 and be done with it. But what if we're close to getting to the next hundredth? What if our digit in the hundredth position is really close to becoming the next digit (so in our case the 8 being really really close to being a 9)? We'd want to show that in our rounding - that while the digit is an 8, it's really closer to 9. So that's what the rules of rounding do - they help determine when we keep the digit we have or we increase the digit by 1. Ok - back to the current question. The hundredth is an 8. The position next to it, in the thousandths, is a 3, so things aren't close to changing that 8 to a 9 (we need to count up 7 more digits - 4, 5, 6, 7, 8, 9, 0 before the hundreds digit becomes a 9). So we leave the hundredths at 8 and the rounded decimal is 8243.88 If however that thousandths digit had been a 5 or bigger (5, 6, 7, 8, 9), then we'd be pretty close to changing the hundredths to a 9 and so we'd then round up to 8234.89.

Zoe Adams · Answer

#8243.88#

#color(blue)("Determine which digits we are going to select")#

I won't go through them all, but this is the structure you're looking for:

#"ten's, units, decimal point, " 1/10 ", " 1/100" , "1/1000...#

Looking at the numbers the ones we will be considering are the green ones in that we have #8/10+8/100#

#color(green)(8243.88)color(red)(316)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("The principle rule about rounding")#

Examine the initial red digit of 3.

If this digit had been #ul("5 or more")# then the last green number of 8 would have been #underline("rounded up")# to 9. So for that condition we would have #8243.89#

However, as the first red digit is #ul("less than 5")# we do not round up the last green digit. So we actually have #8243.88#. They call this #ul("rounding down")#. '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Applying the rounding")#

We round down to give: since the first red digit is less than five.

#color(blue)(8243.88)#