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Rounding Whole Numbers

Rounding Whole Numbers

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Title : Rounding Whole Numbers
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Rounding Whole Numbers

LEARNING OBJECTIVES

  • Round whole numbers to a determined place value
Image of a Best Buy storefront with people walking along the sidewalk that runs in front of the entrance doors.
Best Buy Storefront
The electronics retailer, Best Buy, had 1,0261,026 brick and mortar stores open in October of 20162016. Depending on how this information will be used, it might be enough to say that the company has approximately one thousand stores. The word approximately means that one thousand is not the exact count, but is close to the exact value.
In 20172017, the social network app, Facebook, reported its annual revenue as 40.740.7 billion US dollars. This could mean they actually brought in $40,742,985,316$40,742,985,316 or $40,654,872,131$40,654,872,131. Sometimes the detail is needed, but sometimes just an approximate value is good enough. The real estate app, Zillow, recorded a profit of 1.071.07 billion US dollars; this is an approximate value. If you want to compare Facebook’s 20172017 revenue with Zillow’s 20172017 revenue, the precise dollars or even millions of dollars are unnecessary.
The process of approximating a number is called rounding. Numbers are rounded to a specific place value depending on how much accuracy is needed. Identifying the number of stores owned by Best Buy as approximately 11 thousand means we rounded to the thousands place. Reporting the annual revenue of Facebook as 40.740.7 billion US dollars means we rounded to the hundred millions place. Often the place value to which we round depends on how we will need to use the number.
Using a number line can help us 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 (77 tens) or 8080 (88 tens) 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 a teal dot at the value 76.

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 a teal dot at the value 72.

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 a teal dot at the value 75.
So that everyone rounds the same way in cases like this, mathematicians have agreed to round up to the higher number. 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 76, with an arrow pointed at the seven with the label "tens place", and an arrow pointed at the six with the label "is greater than 5".
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 76 with six slashed through. An arrow points to the six with the label "replace with zero", and an arrow pointed to the seven with the label "add 1". Under the 76 is the number 80. The label says "76 rounded to the nearest ten is 80".
Let’s look again at rounding 7272 to the nearest 1010. Again, we look to the ones place.
An image of value 72, with an arrow pointed at the seven with the label "tens place", and an arrow pointed at the two with the label "is less than 5".
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 72 with two slashed through. An arrow points to the two with the label "replace with zero", and an arrow pointed to the seven with the label "do not add 1". Under the 72 is the number 70.

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 "tens place" and an arrow pointing to the 4
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 843 to the nearest ten gives 840 .