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Round a Number to the Nearest Whole Number or Integer
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Introduction

In this lesson, you will learn how to round a number to the nearest whole number.


This video illustrates the lesson material below. Watching the video is optional.


Decimal Point

A decimal point separates a whole number from the number fragment. Anything after a decimal point is part of a number, not an entire number. Sometimes, you do not want to have the parts of a whole number, you just want to estimate the nearest whole number. Estimating is called rounding.

An image that shows how a decimal point separates a whole number from the number fragment.

Figure 1

Rounding

Sometimes in life, you can’t use decimals. For example, the number of people you are inviting to a party can’t be a decimal number. You can’t have 8.7 people, but you can have 8 or 9 people. Rounding to the nearest whole number is how you deal with problems like this.

The table below shows the rules for whether you round down (for example, from 17.4 to 17) or up (for example, from 17.5 to 18).

Tenths Place How to round to nearest whole number or integer Example
0, 1, 2, 3, 4Keep the number in the one's place

17.4 Rounds to 17

-3.4 rounds to -3

5, 6, 7, 8, 9Increase the number in the one's place by 1

17.5 Rounds to 18

-1.6 Rounds to -2

When rounding to the nearest whole number, look to the tenths place to know where to go. If the tenths place is closer to 0, round down. If the tenths place is closer to 9, round up.

Remember: The place after the decimal is the tenths place.

Example 1

The number line shows a yellow dot on point 1.3. It also shows that it is closer to 1 which means that you will round this number down to 1.

Figure 2

Figure 2 shows 1.3 on a number line. To round to the nearest whole number, determine if 1.3 is closer to 2 or 1. Since 1.3 is closer to 1, you will round this number down to 1.

Example 2

The image shows a number line and a yellow dot on point 1.6. It also shows that it is closer to 2 which means that it should ne rounded up.

Figure 3

Figure 3 shows 1.6 on a number line. Because 1.6 is closer to 2 than to 1, the estimate is 2. According to the rule outlined in the table above, the 6 in the tenths place indicates that it should be rounded up, confirming that the nearest whole number estimation is 2.

Remember: If the number to the right of the decimal point is 5 or greater, round up to the next whole number. If the number to the right of the decimal point is 4 or less, round down to the next whole number.

Example 3

Round 37.4 to the nearest whole number. 37.4 exists between 37 and 38. Because the tenths place is 4 or less, you know to round down. 37.4 can be rounded to 37.

Example 4

Round 18.76 to the nearest whole number. 18.76 exists between 18 and 19. Because the tenths place is 7, which is greater than 5, you know to round up. 18.76 can be rounded to 19.

Rounding to a Negative Integer

These are the rules for rounding positive numbers:

  • If the number in the tenths place is 4 or less, the number in the ones place will stay the same.
  • If the number in the tenths place is 5 or greater, round up.

The rules are slightly different for rounding negative numbers:

  • If the number in the tenths place is 4 or less, the number in the ones place will stay the same.
  • If the number in the tenths place is 5 or greater, the number will round down (further away from 0).

Remember: Once you pass zero on the number line, the numbers become negative. As you move further to the left, the numbers become more negative.

Example 5

Round -3.4 to the nearest integer. Because the tenths place is 4 or less, the ones place will stay the same. -3.4 can be rounded to -3.

If the tenths place was 5 or greater, you would round down (further away from 0) to the next whole number (in this case, -4).

Example 6

The image shows -1.6 on a number line, it also shows that it is closer to -2 so it should be rounded down.

Figure 4

Figure 4 shows -1.6 on a number line. You can see that -1.6 is closer to -2, so you would round -1.6 down to -2.

Note the difference between estimation with positive integers and negative integers. With 1.6, you will go further to the right on the number line (the number would increase), because the tenths place is greater than 5. The estimation would be 2. With -1.6, you’ll do the same thing you did with 1.6, except you will go the opposite direction on the number line (to the left).


Things to Remember


  • When rounding to the nearest whole number, look to the tenths place to know which way to round.
  • When dealing with positive numbers, if the tenths place is 5 or greater, round up to the next number.
  • If the tenths place is 4 or less, the number in the ones place stays the same.

Practice Problems

  1. Round 2.3 to the nearest whole number. (
    Solution
    x
    Solution: 2
    Details:
    To find the answer, start with a number line displaying only the numbers between 0 and 3.
    This is a number line that displays the numbers from zero to three.

    Magnify between points 2 and 3. Magnifying will show the decimals between 2 and 3.
    This is a number line that displays the decimal points between the numbers 2 and 3. There are hash marks evenly spaced along the line. The hash mark on the far left is labeled with the number 2. Going to the right, the next is labeled 2.1. Continuing on they are labeled 2 point 2, 2 point 3, 2 point 4, 2 point 5, 2 point 6, 2 point 7, 2 point 8, 2 point 9. The hash mark on the far left is labeled with the number 3.

    Next, find 2.3.
    This is the same as the previous image except now the number 2 point 3 is highlighted.

    Finally, compare the distances before and after 2.3. You will find that 2.3 is closer to 2 and further away from 3.
    This is the same as the previous image except now there is a line below the number line stretching horizontally from the number 2 to the number 2 point 3. There is another line stretching horizontally from the number 2 point 3 to the number 3. The first line is much shorter than the second line. These lines represent the distance of 2.3 from the number 2 and from the number 3.

    The correct answer is to round to 2.
    )
  2. Round -0.8 to the nearest integer. (
    Solution
    x
    Solution: -1
    Details:
    To find the answer, start with a number line displaying only the numbers between -1 and 1.
    This is a number line that displays the numbers from negative one to one.

    Magnify between the points -1 and 0. Magnifying will show all the negative decimals between -1 and 0.
    This horizontal number line has hash marks spaced evenly. The hash mark on the far left is labeled as negative 1. The next one to the right is negative 0 point 9 followed by negative 0 point 8, negative 0 point 7, negative 0 point 6, negative 0 point 5, negative 0 point 4, negative 0 point 3, negative 0 point 2, negative 0 point 1, and finally the hash mark on the far right is labeled 0.

    Finally, compare the distances before and after -0.8. You will find that -0.8 is closer to -1 and further away from 0.
    This image is the same as the previous one except there is a line below the number line that stretches horizontally from the number negative 1 to the number negative 0 point 8. There is a second horizontal line that is much longer that stretches from the number negative 0 point 8 to the number 0.

    The correct answer is to round to -1.
    )
  3. Round 72 to the nearest whole number. (
    Solution
    x
    Solution:
    72
    )
  4. Round 2.94 to the nearest whole number. ( | Transcript)
  5. Round -24.49999 to the nearest integer. (
    Solution
    x
    Solution:
    -24
    )
  6. Round 42.0201 to the nearest whole number. ( Transcript )

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