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Study Guides > Prealgebra

Rounding Whole Numbers

Learning Outcomes

  • Identify the place value of a digit used for rounding
  • Round a whole number to a specific place value
  In 20132013, the U.S. Census Bureau reported the population of the state of New York as 19,651,12719,651,127 people. It might be enough to say that the population is approximately 2020 million. The word approximately means that 2020 million is not the exact population, but is close to the exact value. The process of approximating a number is called rounding. Numbers are rounded to a specific place value depending on how much accuracy is needed. Saying that the population of New York is approximately 2020 million means we rounded to the millions place. The place value to which we round to depends on how we need to use the number. Using the number line can help you visualize and understand the rounding process. Look at the number line below. Suppose we want to round the number 7676 to the nearest ten. Is 7676 closer to 7070 or 8080 on the number line? We can see that 7676 is closer to 8080 than to 7070. So 7676 rounded to the nearest ten is 8080. An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is an orange dot at the value Now consider the number 7272. Find 7272 on the number line. We can see that 7272 is closer to 7070, so 7272 rounded to the nearest ten is 7070. An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is an orange dot at the value How do we round 7575 to the nearest ten. Find 7575 on the number line. The number 7575 is exactly midway between 7070 and 8080. An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is an orange dot at the value So that everyone rounds the same way in cases like this, mathematicians have agreed to round to the higher number, 8080. So, 7575 rounded to the nearest ten is 8080. Now that we have looked at this process on the number line, we can introduce a more general procedure. To round a number to a specific place, look at the number to the right of that place. If the number is less than 55, round down. If it is greater than or equal to 55, round up. So, for example, to round 7676 to the nearest ten, we look at the digit in the ones place. An image of value The digit in the ones place is a 66. Because 66 is greater than or equal to 55, we increase the digit in the tens place by one. So the 77 in the tens place becomes an 88. Now, replace any digits to the right of the 88 with zeros. So, 7676 rounds to 8080. An image of the value Let’s look again at rounding 7272 to the nearest 1010. Again, we look to the ones place. An image of value The digit in the ones place is 22. Because 22 is less than 55, we keep the digit in the tens place the same and replace the digits to the right of it with zero. So 7272 rounded to the nearest ten is 7070. An image of the value  

Round a whole number to a specific place value

  1. Locate the given place value. All digits to the left of that place value do not change.
  2. Underline the digit to the right of the given place value.
  3. Determine if this digit is greater than or equal to 55.
    • Yes—add 11 to the digit in the given place value.
    • No—do not change the digit in the given place value.
  4. Replace all digits to the right of the given place value with zeros.
 

example

Round 843843 to the nearest ten. Solution
Locate the tens place. The number 843 with the label
Underline the digit to the right of the tens place. The number 843 with the 3 underlined.
Since 33 is less than 55, do not change the digit in the tens place. The number 843 with the 3 underlined.
Replace all digits to the right of the tens place with zeros. The number 840 with the 0 underlined.
Rounding 843843 to the nearest ten gives 840840.
 

try it

Round to the nearest ten: 157157.

Answer: 160160

  Round to the nearest ten: 884884.

Answer: 880880

 

Example

Round each number to the nearest hundred:
  1. 23,65823,658
  2. 3,9783,978

Answer:

1.
Locate the hundreds place. ..
The digit of the right of the hundreds place is 55. Underline the digit to the right of the hundreds place. ..
Since 55 is greater than or equal to 55, round up by adding 11 to the digit in the hundreds place. Then replace all digits to the right of the hundreds place with zeros. .. So 23,658 rounded to the nearest hundred is 23,700.
2.
Locate the hundreds place. ..
Underline the digit to the right of the hundreds place. ..
The digit to the right of the hundreds place is 77. Since 77 is greater than or equal to 55, round up by added 11 to the 99. Then place all digits to the right of the hundreds place with zeros. .. So 3,978 rounded to the nearest hundred is 4,000.

 

try it

Round to the nearest hundred: 17,85217,852.

Answer: 17,90017,900

  Round to the nearest hundred: 4,9514,951.

Answer: 5,0005,000

 

example

Round each number to the nearest thousand:
  1. 147,032147,032
  2. 29,50429,504

Answer:

1.
Locate the thousands place. Underline the digit to the right of the thousands place. ..
The digit to the right of the thousands place is 00. Since 00 is less than 55, we do not change the digit in the thousands place. ..
We then replace all digits to the right of the thousands pace with zeros. .. So 147,032 rounded to the nearest thousand is 147,000.
2.
Locate the thousands place. ..
ⓑUnderline the digit to the right of the thousands place. ..
The digit to the right of the thousands place is 55. Since 55 is greater than or equal to 55, round up by adding 11 to the 99. Then replace all digits to the right of the thousands place with zeros. .. So 29,504 rounded to the nearest thousand is 30,000.
Notice that in part 2, when we add 11 thousand to the 99 thousands, the total is 1010 thousands. We regroup this as 11 ten thousand and 00 thousands. We add the 11 ten thousand to the 33 ten thousands and put a 00 in the thousands place.

    What the video below for more examples of how to round whole numbers to a given place value. https://youtu.be/tpFCYyTi1hc

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