Whole Numbers

Nurses use whole numbers for medication administration, dosage calculation, patient tracking, and many other tasks.To perform these tasks, the nurse needs to understand the concept of whole numbers. Whole numbers are non-negative numbers without any fractional or decimal parts. They start from 0 and go up indefinitely (0, 1, 2, 3, …). They do not have parts like fractions and decimals do such as 2.5 or ⅖.

Learning Objectives

By the end of this section, you will be able to:

  • Identify the place value of a digit
  • Use place value to name whole numbers
  • Use place value to write whole numbers
  • Round whole numbers to a specified place value

Use Place Value with Whole Numbers

The most basic numbers used are the numbers we use to count objects in our world: 1, 2, 3, 4, and so on. These are called the counting numbers. Counting numbers are also called natural numbers. If we add zero to the counting numbers, we get the set of whole numbers.

\phantom{\rule{1.5em}{0ex}}Counting Numbers: 1, 2, 3, …

\phantom{\rule{1.5em}{0ex}}Whole Numbers: 0, 1, 2, 3, …

The notation “…” is called ellipsis and means “and so on,” or that the pattern continues endlessly.

We can visualize counting numbers and whole numbers on a number line. See Figure 1.

The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left. While this number line shows only the whole numbers 0 through 6, the numbers keep going without end.

A horizontal number line with arrows on each end and values of zero to six runs along the bottom of the diagram. A second horizontal line with a left-facing arrow lies above the first and extend from zero to three. This line is labled “smaller”. A third horizontal line with a right-facing arrow lies above the first two, but runs from three to six and is labeled “larger”.
Figure 1

Our number system is called a place value system, because the value of a digit depends on its position in a number. Figure 2 shows the place values. The place values are separated into groups of three, which are called periods. The periods are ones, thousands, millions, billions, trillions, and so on. In a written number, commas separate the periods.

The number 5,278,194 is shown in the chart. The digit 5 is in the millions place. The digit 2 is in the hundred-thousands place. The digit 7 is in the ten-thousands place. The digit 8 is in the thousands place. The digit 1 is in the hundreds place. The digit 9 is in the tens place. The digit 4 is in the ones place.

This figure is a table illustrating the number 5,278,194 within the place value system. The table is shown with a header row, labeled “Place Value”, divided into a second header row labeled “Trillions”, “Billions”, “Millions”, “Thousands” and “Ones”. Under the header “Trillions” are three labeled columns, written from bottom to top, that read “Hundred trillions”, “Ten trillions” and “Trillions”. Under the header “Billions” are three labeled columns, written from bottom to top, that read “Hundred billions”, “Ten billions” and “Billions”. Under the header “Millions” are three labeled columns, written from bottom to top, that read “Hundred millions”, “Ten millions” and “Millions”. Under the header “Thousands” are three labeled columns, written from bottom to top, that read “Hundred thousands”, “Ten thousands” and “Thousands”. Under the header “Ones” are three labeled columns, written from bottom to top, that read “Hundreds”, “Tens” and “Ones”. From left to right, below the columns labeled “Millions”, “Hundred thousands”, “Ten thousands”, “Thousands”, “Hundreds”, “Tens”, and “Ones”, are the following values: 5, 2, 7, 8, 1, 9, 4. This means there are 5 millions, 2 hundred thousands, 7 ten thousands, 8 thousands, 1 hundreds, 9 tens, and 4 ones in the number five million two hundred seventy-nine thousand one hundred ninety-four.
Figure 2

EXAMPLE 1

In the number 63,407,218, find the place value of each digit:

  1. 7
  2. 0
  3. 1
  4. 6
  5. 3
Solution

Place the number in the place value chart:

This figure is a table illustrating the number 63,407,218 within the place value system. The table is shown with a header row, labeled “Place Value”, divided into a second header row labeled “Trillions”, “Billions”, “Millions”, “Thousands” and “Ones”. Under the header “Trillions” are three labeled columns, written from bottom to top, that read “Hundred trillions”, “Ten trillions” and “Trillions”. Under the header “Billions” are three labeled columns, written from bottom to top, that read “Hundred billions”, “Ten billions” and “Billions”. Under the header “Millions” are three labeled columns, written from bottom to top, that read “Hundred millions”, “Ten millions” and “Millions”. Under the header “Thousands” are three labeled columns, written from bottom to top, that read “Hundred thousands”, “Ten thousands” and “Thousands”. Under the header “Ones” are three labeled columns, written from bottom to top, that read “Hundreds”, “Tens” and “Ones”. From left to right, below the columns labeled “Ten millions”, “Millions”, “Hundred thousands”, “Ten thousands”, “Thousands”, “Hundreds”, “Tens”, and “Ones”, are the following values: 6, 3, 4, 0, 7, 2, 1, 8. This means there are 6 ten millions, 3 millions, 4 hundred thousands, 0 ten thousands, 7 thousands, 2 hundreds, 1 ten, and 8 ones in the number sixty-three million, four hundred seven thousand, two hundred eighteen.

a) The 7 is in the thousands place.
b) The 0 is in the ten thousands place.
c) The 1 is in the tens place.
d) The 6 is in the ten-millions place.
e) The 3 is in the millions place.

TRY IT 1.1

This figure is a table illustrating the place value system. The table is shown with a header row, labeled “Place Value”, divided into a second header row labeled “Trillions”, “Billions”, “Millions”, “Thousands” and “Ones”. Under the header “Trillions” are three labeled columns, written from bottom to top, that read “Hundred trillions”, “Ten trillions” and “Trillions”. Under the header “Billions” are three labeled columns, written from bottom to top, that read “Hundred billions”, “Ten billions” and “Billions”. Under the header “Millions” are three labeled columns, written from bottom to top, that read “Hundred millions”, “Ten millions” and “Millions”. Under the header “Thousands” are three labeled columns, written from bottom to top, that read “Hundred thousands”, “Ten thousands” and “Thousands”. Under the header “Ones” are three labeled columns, written from bottom to top, that read “Hundreds”, “Tens” and “Ones”. The row underneath the place value labels is blank.
Place Value Chart

TRY IT 1.2

This figure is a table illustrating the place value system. The table is shown with a header row, labeled “Place Value”, divided into a second header row labeled “Trillions”, “Billions”, “Millions”, “Thousands” and “Ones”. Under the header “Trillions” are three labeled columns, written from bottom to top, that read “Hundred trillions”, “Ten trillions” and “Trillions”. Under the header “Billions” are three labeled columns, written from bottom to top, that read “Hundred billions”, “Ten billions” and “Billions”. Under the header “Millions” are three labeled columns, written from bottom to top, that read “Hundred millions”, “Ten millions” and “Millions”. Under the header “Thousands” are three labeled columns, written from bottom to top, that read “Hundred thousands”, “Ten thousands” and “Thousands”. Under the header “Ones” are three labeled columns, written from bottom to top, that read “Hundreds”, “Tens” and “Ones”. The row underneath the place value labels is blank.
Place Value Chart

When you write a check, you write out the number in words as well as in digits. To write a number in words, write the number in each period, followed by the name of the period, without the s at the end. Start at the left, where the periods have the largest value. The ones period is not named. The commas separate the periods, so wherever there is a comma in the number, put a comma between the words (see Figure 3). The number 74,218,369 is written as seventy-four million, two hundred eighteen thousand, three hundred sixty-nine.

In this figure, the numbers 74, 218 and 369 are listed in a row, separated by commas. Each number has a curly bracket beneath it with the word “millions” written below the number 74, “thousands” written below the number 218, and “ones” written below the number 369. A left-facing arrow points at these three words, labeling them “periods”. One row down is the number “74”, a right-facing arrow and the words “Seventy-four million” followed by a comma. The next row below is the number “218”, a right-facing arrow and the words “two hundred eighteen thousand” followed by a comma. On the bottom row is the number “369”, a right-facing arrow and the words “three hundred sixty-nine”.
Figure 3

HOW TO: Name a Whole Number in Words.

  1. Start at the left and name the number in each period, followed by the period name.
  2. Put commas in the number to separate the periods.
  3. Do not name the ones period.

EXAMPLE 2

Name the number 8,165,432,098,710 using words.

Solution

Name the number in each period, followed by the period name.

In this figure, the numbers 8, 165, 432, 098 and 710 are listed in a row, separated by commas. Each number has a horizontal bracket beneath with the word “trillions” written below the number 8, “billions” written below the number 165, “millions” written below the number 432, “thousands” written below the number 098, and “ones” written below the number 710. One row down is the number 8, a right-facing arrow and the words “Eight trillion” followed by a comma. On the next row below is the number 165, a right-facing arrow and the words “One hundred sixty-five billion” followed by a comma. On the next row below is the number 432, a right-facing arrow and the words “Four hundred thirty-two million” followed by a comma. On the next row below is the number “098”, a right-facing arrow and the words “Ninety-eight thousand” followed by a comma. On the bottom row is the number 710, a right-facing arrow and the words “Seven hundred ten”.

Put the commas in to separate the periods.

So, 8,165,432,098,710 is named as eight trillion, one hundred sixty-five billion, four hundred thirty-two million, ninety-eight thousand, seven hundred ten.

TRY IT 2.1

This figure is a table illustrating the place value system. The table is shown with a header row, labeled “Place Value”, divided into a second header row labeled “Trillions”, “Billions”, “Millions”, “Thousands” and “Ones”. Under the header “Trillions” are three labeled columns, written from bottom to top, that read “Hundred trillions”, “Ten trillions” and “Trillions”. Under the header “Billions” are three labeled columns, written from bottom to top, that read “Hundred billions”, “Ten billions” and “Billions”. Under the header “Millions” are three labeled columns, written from bottom to top, that read “Hundred millions”, “Ten millions” and “Millions”. Under the header “Thousands” are three labeled columns, written from bottom to top, that read “Hundred thousands”, “Ten thousands” and “Thousands”. Under the header “Ones” are three labeled columns, written from bottom to top, that read “Hundreds”, “Tens” and “Ones”. The row underneath the place value labels is blank.
Place Value Chart

TRY IT 2.2

This figure is a table illustrating the place value system. The table is shown with a header row, labeled “Place Value”, divided into a second header row labeled “Trillions”, “Billions”, “Millions”, “Thousands” and “Ones”. Under the header “Trillions” are three labeled columns, written from bottom to top, that read “Hundred trillions”, “Ten trillions” and “Trillions”. Under the header “Billions” are three labeled columns, written from bottom to top, that read “Hundred billions”, “Ten billions” and “Billions”. Under the header “Millions” are three labeled columns, written from bottom to top, that read “Hundred millions”, “Ten millions” and “Millions”. Under the header “Thousands” are three labeled columns, written from bottom to top, that read “Hundred thousands”, “Ten thousands” and “Thousands”. Under the header “Ones” are three labeled columns, written from bottom to top, that read “Hundreds”, “Tens” and “Ones”. The row underneath the place value labels is blank.
Place Value Chart
We reverse the process by writing the digits from the name of the number. To write the number in digits, we first look for the clue words that indicate the periods. It is helpful to draw three blanks for the needed periods and then fill in the blanks with the numbers, separating the periods with commas.

HOW TO: Write a Whole Number Using Digits.

  1. Identify the words that indicate periods. (Remember, the ones period is never named.)
  2. Draw three blanks to indicate the number of places needed in each period. Separate the periods by commas.
  3. Name the number in each period and place the digits in the correct place value position.

EXAMPLE 3

Write nine billion, two hundred forty-six million, seventy-three thousand, one hundred eighty-nine as a whole number using digits.

Solution

Identify the words that indicate periods.
Except for the first period, all other periods must have three places. Draw three blanks to indicate the number of places needed in each period. Separate the periods by commas.
Then write the digits in each period.

An image has two lines of text. The upper lines read “nine billion”, followed by a comma, and “two hundred forty six million”, also followed by a comma. The words “billion” and “million” are underlined and each phrase has a curly bracket underneath. The lower lines read “seventy three thousand”, followed by a comma, and “one hundred eighty nine”. The word “thousand” is underlined and each phrase has a curly bracket underneath.

The number is 9,246,073,189.

TRY IT 3.1

TRY IT 3.2

In 2022, The United States Census Bureau estimated the population of Phoenix as 1,644,409. We could say the population of Phoenix was approximately 1.6 million. In many cases, you don’t need the exact value; an approximate number is good enough.

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 Phoenix is approximately 1.6 million means that we rounded to the hundred thousands place.

EXAMPLE 4

Round 23,658 to the nearest hundred.

Solution
Step Example Demonstration

1. Locate the given place value with an arrow. All digits to the left do not change.

 Locate the hundreds place in 23,658. An arrow points to the number 6 in 23,658.

2. Underline the digit to the right of the given place value.

 Underline the 5, which is to the right of the hundreds place (in the tenths place). The number 5 in 23,658 is identified with a underline.

3. Is this digit 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.

 Add 1 to the 6 in the hundreds place, since 5 is greater than or equal to 5. An arrow points to the number 6 in 23,658, indicating to add 1 to this number

4. Replace all digits to the right of the given place value with zeros.

 Replace all digits to the right of the hundreds place with zeros. An arrow points to the number 7 in 23,700, indicating that 1 has been added. The final two digits from the starting number have been replaced with zeroes.

So, 23,658 rounded to the nearest hundred is 23,700.

TRY IT 4.1

TRY IT 4.2

HOW TO: Round Whole Numbers.

  1. Locate the given place value and mark it with an arrow. All digits to the left of the arrow do not change.
  2. Underline the digit to the right of the given place value.
  3. Is this digit 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.

EXAMPLE 5

Round 103,978 to the nearest:

  1. hundred
  2. thousand
  3. ten thousand
Solution

a)

Locate the hundreds place in 103,978. In the number 103,978, an arrow indicates the number 9 is in the hundreds place.
Underline the digit to the right of the hundreds place. In the number 103,978, the number 7 is underlined to indicate it will be used to decide whether to round the number 9 up or leave it as is.
Since 7 is greater than or equal to 5, add 1 to the 9. Replace all digits to the right of the hundreds place with zeros. In the number 103,978, a red arrow indicates the 9 should be rounded up. Because the 9 must be replaced with 10, 1 is added to the number 3, changing it to 4; and the number 9 is replaced with a zero.

So, 103,978 rounded to the nearest hundred is 104,000.

b)

Locate the thousands place and underline the digit to the right of the thousands place. In the number 103,978, an arrow points to the 3 and identifies it as the thousands place, and the number 9 is underlined, indicating it should be rounded up or down.
Since 9 is greater than or equal to 5, add 1 to the 3. Replace all digits to the right of the hundreds place with zeros. In the number 103, 978, an arrow indicates the number 3 should be rounded up to 4, and a second arrow indicates the numbers to the right of 4 should be replaced with zeroes.

So, 103,978 rounded to the nearest thousand is 104,000.

c)

Locate the ten thousands place and underline the digit to the right of the ten thousands place. The number 103,978 has an arrow pointing to the 0, indicating it is in the ten thousands place, and the 3 is underlined, indicating it should be rounded up or down.
Since 3 is less than 5, we leave the 0 as is, and then replace the digits to the right with zeros. The number 100,000.

So, 103,978 rounded to the nearest ten thousand is 100,000.

TRY IT 5.1

TRY IT 5.2

Key Concepts

  • Place Value as in Figure 2.
  • Name a Whole Number in Words
    1. Start at the left and name the number in each period, followed by the period name.
    2. Put commas in the number to separate the periods.
    3. Do not name the ones period.
  • Write a Whole Number Using Digits
    1. Identify the words that indicate periods. (Remember the ones period is never named.)
    2. Draw 3 blanks to indicate the number of places needed in each period. Separate the periods by commas.
    3. Name the number in each period and place the digits in the correct place value position.
  • Round Whole Numbers
    1. Locate the given place value and mark it with an arrow. All digits to the left of the arrow do not change.
    2. Underline the digit to the right of the given place value.
    3. Is this digit 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.

Glossary

counting numbers
The counting numbers are the numbers 1, 2, 3, …
whole numbers
The whole numbers are the numbers 0, 1, 2, 3, ….

Practice Makes Perfect

Use Place Value with Whole Numbers

PRACTICE: Find the place value of each digit in the given numbers.

PRACTICE: Name the numbers using words.

PRACTICE: Write numbers using digits.

PRACTICE: Round numbers to the specified place.

PRACTICE: Everyday math.

Chapter Attributions

This chapter was adapted by Cheryl Colan from “1.1 Whole Numbers” in Introductory Algebra by Izabela Mazur. Licensed under a CC BY 4.0 license.

License

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College Mathematics Review for Nursing Students Copyright © 2024 by Phoenix College Nursing is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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