# What is 8243.88316 rounded to the nearest hundredth?

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.

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

Examine the initial red digit of 3.

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

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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