Introduction

In this lesson, you will learn how to round a number to a specified precision. When rounding a number to the nearest whole number, you look to the tenths place to tell you where to go, up or down. You can use this rule to round to any nearest number, not just the nearest whole number.

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

• Rounding to Any Place Value (06:41 mins) | Transcript

Rounding to Any Place

When rounding to the nearest whole number, you looked at the tenths place and decided if you needed to round up or down. When rounding to the nearest tens or hundreds place, you would look at the number to the right and, using the same rules as before, round up or down.

Example 1
428.763

If you wanted to round to the ones place, you see the 7 in the tenths place and that tells us that you need to round up to 429. If you would like to round to the tens place, you need to look at the ones place.

Figure 1

Figure 1 shows 428.763 on a number line. If you want to round to the tens place, look at the ones place and, using the same rules established earlier, make a decision to go up to 430 or go down to 420. In this example, the number in the ones place is 8, which is greater than 5. This means that you round up in the tens position to 430.

If the number was 423, you would round this number to 420 because the number in the ones place is a 3.

You can round a number to any place.

Example 2
Round 428.763 to the hundreds place.

In order to do this, look at the number to the right of the hundreds place, which is 2, and then decide which way to round. Because 2 is less than 4, you would round down to 400.

Figure 2

Now round 428.763 to the nearest tenths. Look at the hundredths place, which is 6. Since 6 is greater than 5, round up to 428.8.

You can round to any place by following the rounding rules.

Figure 3

Example 3

Round 301.09 to the ones and tenths place using the rules of rounding. For the ones place, look at the place value to the right, which is the tenths place. Since it is 0, you do not round up. It remains 301. For the tenths place, look at the hundredths place value, 9. Since 9 is greater than 5, round up to the nearest tenths: 301.1.

Figure 4

You may get an answer that has a very long list of decimals, like 3.1415926535897932…. You don’t want to have to write that all of the time, but ending it early causes you to lose some precision. 3 is not the same as 3.14, which is not the same as 3.1415. Precision is the number of decimal places you keep on the number. The more you keep, the closer your number is to the correct number. In many problems you’ll be solving in future lessons, you’ll be asked to round your answer to a certain precision.

Remember, when rounding, look at the digit to the right of the place value you want to round to (if you’re rounding to the tenths place, look at the hundredths place), if it’s less than or equal to 4 the place value you are rounding to stays the same. If the place value to the right is greater than or equal to 5, add 1 to the place value you are rounding to.

Things to Remember

• You can round any number to any place by following the rules.

Practice Problems

1. Round 227.18 to the nearest ten. (
   Video Solution

   x

   Solution: 230
   Details:
   

   
   (Round a Number to a Specified Precision #1 (01:32 mins) | Transcript)
   | Transcript)
2. Round 27070 to the nearest hundred. (
   Solution

   x

   Solution: 27100
   Details:
    
   The zero is in the hundreds place.
   \(27,{\color{red}0}70\)
   
   To the right of 0 is the number 7.
   \(27,{\color{red}0}{\color{orange}7}0\)
   
   To determine if 0 is to be increased, look at the position of the number 7 on the number line. Since the number 7 is higher than 5, you will increase 0 by 1, which is 1.
   
   
   After increasing the 0 to 1 in the hundreds place, turn all the numbers to the right of the hundreds place into zeros.
   \(27,{\color{red}1}00\)
   
   The rounded answer is 27100.
   )
3. Round 47397686 to the nearest million. (
   Solution

   x

   Solution: 47000000
   Details:
    
   
   Look at the 7 in the millions place.
   \(4{\color{red} 7}397686\)
   
   To determine if 7 is to be increased by one or stay the same, look at the number on the right.
   To the right of 7 is the number 3.
   \(4{\color{red} 7}{\color{orange} 3}97686\)
   
   The number 3 is less than 5, so the number 7 will not increase and will just stay the same.
   
   
   
   After determining that the number 7 in the millions place will not change, turn all the numbers to the right of the 7 into zeros.
   \(4{\color{red} 7}000000\)
   
   The rounded answer is 47,000,000.
   )
4. Round 0.62968 to the nearest hundredth. (
   Solution

   x

   Solution:
   0.63
   )
5. Round 856.861203 to the nearest thousandth. (
   Solution

   x

   Solution:
   856.861
   )
6. Round 599.495 to the nearest tenth. (
   Video Solution

   x

   Solution: 599.5
   Details:
   

   
   (Round a Number to a Specified Precision #6 (01:54 mins) | Transcript)
   Transcript)
7. Round 599.995 to the nearest tenth. (
   Solution

   x

   Solution:
   600
   )

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