# Rounding Numbers

Rounding numbers is a good way to estimate about how much you have. Rounded numbers are not exact numbers, but they are close to the actual amount of something. For example, you might have \$59.91 and say “I have \$60” because \$59.91 is very close to \$60. So, it’s not the exact amount you have, but it’s close. You can round numbers to various place values, which is how it’s related to the place values mentioned earlier.

There are several things you need to do in order to round a number. First, locate the digit you are rounding. Let’s say it’s the hundreds digit.

1. Locate the digit directly after the digit you want to round. In our example, since we want to round the 100's digit, we would look at the 10's digit.
2. If the digit after the digit you want to round is less than five (that means, 0, 1, 2, 3, 4) then you will leave the digit you want to round alone, and turn all the following digits into zeroes.
3. If the digit after the digit you want to round is five, or greater (that means, 5, 6, 7, 8, 9) then you will increase the digit you want to round by 1. The digits following the digit you’re rounding will still convert to zeroes.

Here is a number line showing what we just explained. The red numbers (1, 2, 3 and 4) get rounded down, so if the digit you're looking at is one of those numbers, the digit you're rounding stays the same, and all digits after that one become zeroes. The green numbers (5, 6, 7, 8 and 9) get rounded up, so if the digit you're looking at is one of those numbers, the digit you're rounding is increased by 1 (if the digit is 7, it becomes 8, and so on). Let’s look at a couple examples of this.

Example 1: Round 3,594 to the nearest tens’ digit. We have circled the number we want to round, which is the tens’ digit, and then we underlined the digit after it, which is the ones’ digit. We want to look at the ones’ digit. We see that it is a 4. That means that we leave the digit we’re rounding absolutely alone—we don’t change it at all. Then we change every digit after the digit we’ve rounded into a zero (0). Our newly rounded number would look like this: As you can see, the thousands’ and hundreds’ digits stayed completely the same. The tens’ digit was rounded, and it ended up staying the same as well. The ones’ digit, which we had to consider in order to do our rounding, turned into a zero. We would say, in math, that this number “rounds down” because we didn’t have to increase the digit we were rounding.

Let’s try another example.

Example 2: Round 20,385 to the hundreds’ digit. We have circled the 100's digit, and then we underlined the next digit to the right, which is the tens’ digit, so that we know which number we’re looking at. Looking at the tens’ digit, we see that it is 8, which is greater than 5, meaning we have to round up. In order to round up, we increase the hundreds’ digit by 1. This means that, since the hundreds’ digit is 3, we would increase it to 4. Now, the next digits (tens’ digit and ones’ digit) are converted into zeroes. Our rounding would look like this: As you can see, the hundreds’ digit increased by 1, and the following digits changed into zeroes. Thus, our rounded number is 20,400.

We’ll try one more—this time we’ll give you an example, and when you get the rounded answer you can type it into the box below to see if you’re correct!

Round 83,597 to the hundreds’ digit.
First, locate the 100's digit and circle it. The 5 should be circled. Then locate the digit next to it—to the right—in this example it is a 9. Since 9 is greater than 5, you would round up, which means increase the 100's digit by one and turn the following digits into zero. You can see that we’ve done this by increasing the 5 to a 6, and changing the 9 and 7 both into zeroes. Thus, you end up with 83,600.
83600

## Rounding Decimals

Rounding decimals is exactly like rounding whole numbers, except you’ll be asked to round to place values after the decimal instead of before. It still works the same way—you’ll still have to locate the digit you’re rounding, look at the following digit, decide if it rounds up or rounds down, and then change the following digits to zeroes.

Here’s an example: Round 3.4985 to the thousandths’ digit.

First, locate the thousandths digit, like this: Notice that we have circled the thousandths digit, and then underlined the next digit, which we need to look at in order to determine how to round our number. Remember, if the digit after the digit we’re rounding is less than 5 (that means 0, 1, 2, 3, 4) then we round down, and the digit we’re rounding stays the same. If the digit after the digit we’re rounding is 5 or greater (that means 5, 6, 7, 8, 9) that means we round up—rounding up is when you increase the digit you’re rounding by 1.

In this example, we notice that the underlined digit is an 8, which is greater than 5. That means we’re going to round up for this one. The 8 becomes a 9, and the 5 becomes a 0. Thus, our final rounded number is 3.4990.

Let’s try one more example of rounding with decimals. This time, we’ll give you a number, and you can round it. Then, when you’re done rounding, type it in to the answer box and check your answer with ours.

Round 9.1258 to the tenths’ digit.
In order to round to the tenths’ digit, we would circle the 1 (which is the tenths’ digit) and underline the 2 (which follows the tenths’ digit). We would look at the underlined number, 2, and see that it’s less than five; therefore, we would round down. Rounding down means leaving the 1 alone, and changing all of the following digits into zeroes, giving us 9.1000 as our answer.
{9.1000|9.1|9.10|9.100}

## Rounding Fractions

Rounding fractions usually means deciding whether the fraction is greater or less than one half. If the fraction is less than one half, the fraction rounds down, and you are left with just a whole number (and no fraction). If the fraction is equal to or larger than one half, it would round up, and you will increase the whole number by one. For example, 1/3 is less than one half, so it would round down. 7/8 is greater than one half, so it would round up. Follow along with the next few examples:

Example: Round 5 1/5 to the nearest whole number.

1. Decide if 1/5 is smaller than, equal to, or greater than 1/2. We know that 1/5 is smaller than 1/2.

2. Since we realized that 1/5 is smaller than 1/2, we know that this number is going to round down.

3. Rounding down means keeping the whole number the same, and dropping off the fraction. Thus, 5 1/5 rounded down equals 5.

### What if you can't easily tell if the fraction is more or less than 1/2?

Example: Round 3 18/34 to the nearest whole number.

Note: It’s not always easy to tell whether your fraction is greater than, equal to, or less than 1/2. As with this fraction, we might not know right away whether 18/34 is greater than, equal to, or less than 1/2. In this type of situation, you have two options:

1. If your denominator is an even number (divisible by 2), figure out what 1/2 would be using the denominator of the fraction you’re given. For this example, you would figure out that 1/2 of 34 is 17, so 17/34 = 1/2. Then, you would compare 17/34 to 18/34 and realize that 18/34 is greater, so your whole number would round up.

2. If your denominator is an odd number, multiply the fraction by 2/2. This makes the denominator an even number. Then, follow the directions listed previously in option 1. Note that you do not have to do this for this example, because the denominator is already an even number. You would only follow this step if your denominator were an odd number. We’ll give you an example of this next.

Now that you’ve determined that 18/34 is greater than 1/2, you can round up. Your original whole number was 3, so rounding up would take it to 4. Thus, your final (rounded) answer is 4.

Now, we’ll try an example with an odd denominator. Let’s round 9 5/7 to the nearest whole number.

First, multiply the fraction, 5/7, by 2/2. When you multiply 5/7 x 2/2, you get 10/14. Now, you need to figure out what 1/2 would look like with a denominator of 14. To do that, simply figure out half of 14 (7) and use it as the numerator, so it becomes 7/14. Now, compare 10/14 to 7/14 and realize that 10/14 is larger than 7/14. This means you will be rounding up. Think back to your original whole number, which is 9. If you increase 9 by 1, you would get 10. Thus, your rounded, final answer is 10.

If any of the work with fractions didn’t make sense, please read through our page on Multiplying Fractions.

## Rounding in Estimation

Why is rounding important in estimation? Many times, you will be asked to use your rounding skills in order to estimate amounts or costs of things; how many of something you might need, how much your bill will be at a store or restaurant, and so on. It’s important to be able to round these numbers so that it doesn’t take you a long time to figure out a total bill for example; at the same time you want to be fairly accurate in your estimation, because if you estimate too high or too low you’ll end up thinking that you’re paying a price far different from what you’ll actually be paying. We’ll give you several examples here so that you’ll be prepared to do this as well.

Example 1: At the store, you need to get a cucumber, onions, 3 peppers, strawberries, bananas, and oranges. The cucumber is \$1.09. The onions are \$3.99 for a 5 lb bag. The peppers are \$1.49 each. Strawberries are \$2.99 per pound, and you get 2 lbs. Bananas are 79¢ per pound and you get 3 lbs. Oranges are \$4.99 per 5 lb bag, so you get one bag. Estimate your total, before tax, at the store.

Solution: Most of these prices can be rounded. When rounding money, we usually round to the nearest dollar. Sometimes, though, we round to the half dollar. This is a judgment call, unless it specifically tells you what to round to. In this example, we will be rounding to both the nearest dollar and the nearest half dollar.

Here’s how we’ll round the items—more than \$.50 rounds up, less than \$.50 rounds down; however, if there is something in the \$.40s or \$.60s, we’ll round to the nearest half dollar, like this:

The cucumber is \$1.09, this rounds down to \$1.

The onions are \$3.99, this rounds up to \$4.

The peppers are \$1.49 each, we’re going to round them to \$1.50 each. Now we multiply by 3, so we are going to spent approximately \$4.50 on peppers.

Strawberries are \$2.99 per pound, this rounds to \$3 per pound, and you get 2 lbs, so you spend about \$6 on strawberries.

Bananas are 79¢ per pound, we’re going to round this to \$1 per lb, and you get 3 lbs, so you spend about \$3 on bananas.

Oranges are \$4.99 per 5 lb bag, so we’re going to round to this to \$5.

Now that we’ve rounded all our numbers, we can quickly add them together, like this:

\$1 + \$4 + \$4.50 + \$6 + \$3 + \$5 = \$23.50

So, our estimated total for this trip to the grocery store is \$23.50. Remember, this is an estimate—it is not exactly what your total would be—but it is very close.

Example 2: You are planning a party for a large number of people. In the treat bags, you would like to put 4 pieces of candy. You have had 142 people RSVP yes, that they’ll be at the party. If one bag of candy contains 125 pieces, how many bags will you need to make enough treat bags for everyone?

First, you need to figure out how many pieces of candy you will need. In order to do this, you would multiply the number of people times the number of candies going into each bag. However, you would get a problem that says 142 x 4. Instead of trying to do this problem, you would round 142 to 150 (always round up when planning on having at least enough) and then you can do 150 x 4 using mental math—you’d get 600. Therefore, you know you need 600 pieces of candy.

Now, you need to divide 600 by the amount of candy in each bag—125. You should not round this number, because it is an exact number in each bag. Once you divide, you get 4 r 100. Think about what a remainder means in this problem. The remainder would be additional pieces of candy you would need. Therefore, you would need to change the 4 bags into 5—to make sure you have enough (this is rounding up). So, you would actually be buying 5 bags of candy, giving you 625 pieces of candy, but you know you would have enough.

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