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1.1 Introduction to whole numbers  (Page 4/13)

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Write each number in standard form:

fifty-three million, eight hundred nine thousand, fifty-one.

53,809,051

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Write each number in standard form:

two billion, twenty-two million, seven hundred fourteen thousand, four hundred sixty-six.

2,022,714,466

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A state budget was about $77 billion. Write the budget in standard form.

Solution

Identify the periods. In this case, only two digits are given and they are in the billions period. To write the entire number, write zeros for all of the other periods.
An image with four blocks of text pointing to numerical values. The first block of text is “77 billion”, has the label “billions”, and points to value “77”. The second block of text is null, has the label “millions”, and points to value “000”. The third block of text is null, has the label “thousands”, and points to value “000”. The fourth block of text is null, has the label “ones”, and points to the value “000”.

So the budget was about $77,000,000,000.

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Write each number in standard form:

The closest distance from Earth to Mars is about 34 million miles.

34,000,000 miles

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Write each number in standard form:

The total weight of an aircraft carrier is 204 million pounds.

204,000,000 pounds

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Round whole numbers

In 2013 , the U.S. Census Bureau reported the population of the state of New York as 19,651,127 people. It might be enough to say that the population is approximately 20 million. The word approximately means that 20 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 20 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 in [link] . Suppose we want to round the number 76 to the nearest ten. Is 76 closer to 70 or 80 on the number line?

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 “76” on the number line.
We can see that 76 is closer to 80 than to 70 . So 76 rounded to the nearest ten is 80 .

Now consider the number 72 . Find 72 in [link] .

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 “72” on the number line.
We can see that 72 is closer to 70 , so 72 rounded to the nearest ten is 70 .

How do we round 75 to the nearest ten. Find 75 in [link] .

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 “75” on the number line.
The number 75 is exactly midway between 70 and 80 .

So that everyone rounds the same way in cases like this, mathematicians have agreed to round to the higher number, 80 . So, 75 rounded to the nearest ten is 80 .

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 5 , round down. If it is greater than or equal to 5 , round up.

So, for example, to round 76 to the nearest ten, we look at the digit in the ones place.

An image of value “76”. The text “tens place” is in blue and points to number 7 in “76”. The text “is greater than 5” is in red and points to the number 6 in “76”.

The digit in the ones place is a 6 . Because 6 is greater than or equal to 5 , we increase the digit in the tens place by one. So the 7 in the tens place becomes an 8 . Now, replace any digits to the right of the 8 with zeros. So, 76 rounds to 80 .

An image of the value “76”. The “6” in “76” is crossed out and has an arrow pointing to it which says “replace with 0”. The “7” has an arrow pointing to it that says “add 1”. Under the value “76” is the value “80”.

Let’s look again at rounding     72 to the nearest 10 . Again, we look to the ones place.

An image of value “72”. The text “tens place” is in blue and points to number 7 in “72”. The text “is less than 5” is in red and points to the number 2 in “72”.

The digit in the ones place is 2 . Because 2 is less than 5 , we keep the digit in the tens place the same and replace the digits to the right of it with zero. So 72 rounded to the nearest ten is 70 .

An image of the value “72”. The “2” in “72” is crossed out and has an arrow pointing to it which says “replace with 0”. The “7” has an arrow pointing to it that says “do not add 1”. Under the value “72” is the value “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 5 .
    • Yes—add 1 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.
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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