What Is the Next Whole Number After One Hundred Thousand

Whole Numbers

2 Introduction to Whole Numbers

Learning Objectives

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

• Identify counting numbers and whole numbers
• Model whole numbers
• Identify the place value of a digit
• Use place value to name whole numbers
• Use place value to write whole numbers
• Round whole numbers

Identify Counting Numbers and Whole Numbers

Learning algebra is similar to learning a language. You start with a basic vocabulary and then add to it as you go along. You need to practice often until the vocabulary becomes easy to you. The more you use the vocabulary, the more familiar it becomes.

Algebra uses numbers and symbols to represent words and ideas. Let's look at the numbers first. The most basic numbers used in algebra are those we use to count objects: and so on. These are called the counting numbers. The notation "…" is called an ellipsis, which is another way to show "and so on", or that the pattern continues endlessly. Counting numbers are also called natural numbers.

Doing the Manipulative Mathematics activity Number Line-Part 1 will help you develop a better understanding of the counting numbers and the whole numbers.

Counting Numbers

The counting numbers start with and continue.

Counting numbers and whole numbers can be visualized on a number line as shown in (Figure).

The numbers on the number line increase from left to right, and decrease from right to left.

The point labeled is called the origin. The points are equally spaced to the right of and labeled with the counting numbers. When a number is paired with a point, it is called the coordinate of the point.

The discovery of the number zero was a big step in the history of mathematics. Including zero with the counting numbers gives a new set of numbers called the whole numbers.

Whole Numbers

The whole numbers are the counting numbers and zero.

We stopped at when listing the first few counting numbers and whole numbers. We could have written more numbers if they were needed to make the patterns clear.

Which of the following are ⓐ counting numbers? ⓑ whole numbers?

Solution

The numbers and are neither counting numbers nor whole numbers. We will discuss these numbers later.

Which of the following are ⓐ counting numbers ⓑ whole numbers?

• ⓐ 2, 9, 241, 376
• ⓑ 0, 2, 9, 241, 376

Which of the following are ⓐ counting numbers ⓑ whole numbers?

• ⓐ 7, 13, 201
• ⓑ 0, 7, 13, 201

Model Whole Numbers

Our number system is called a place value system because the value of a digit depends on its position, or place, in a number. The number has a different value than the number Even though they use the same digits, their value is different because of the different placement of the and the and the

Money gives us a familiar model of place value. Suppose a wallet contains three bills, seven bills, and four bills. The amounts are summarized in (Figure). How much money is in the wallet?

Find the total value of each kind of bill, and then add to find the total. The wallet contains

Base-10 blocks provide another way to model place value, as shown in (Figure). The blocks can be used to represent hundreds, tens, and ones. Notice that the tens rod is made up of ones, and the hundreds square is made of tens, or ones.

(Figure) shows the number modeled with blocks.

We use place value notation to show the value of the number

Digit	Place value	Number	Value	Total value
	hundreds
	tens
	ones

Use place value notation to find the value of the number modeled by the blocks shown.

Use place value notation to find the value of the number modeled by the blocks shown.

176

Use place value notation to find the value of the number modeled by the blocks shown.

237

Doing the Manipulative Mathematics activity "Model Whole Numbers" will help you develop a better understanding of place value of whole numbers.

Identify the Place Value of a Digit

By looking at money and blocks, we saw that each place in a number has a different value. A place value chart is a useful way to summarize this information. The place values are separated into groups of three, called periods. The periods are ones, thousands, millions, billions, trillions, and so on. In a written number, commas separate the periods.

Just as with the blocks, where the value of the tens rod is ten times the value of the ones block and the value of the hundreds square is ten times the tens rod, the value of each place in the place-value chart is ten times the value of the place to the right of it.

(Figure) shows how the number is written in a place value chart.

Solution

Write the number in a place value chart, starting at the right.

• ⓐ ten millions
• ⓑ tens
• ⓒ hundred thousands
• ⓓ millions
• ⓔ ones

• ⓐ billions
• ⓑ ten thousands
• ⓒ tens
• ⓓ hundred thousands
• ⓔ hundred millions

Use Place Value to Name Whole Numbers

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 with the digit at the left, which has the largest place value. The commas separate the periods, so wherever there is a comma in the number, write a comma between the words. The ones period, which has the smallest place value, is not named.

So the number is written thirty-seven million, five hundred nineteen thousand, two hundred forty-eight.

Notice that the word and is not used when naming a whole number.

Name a whole number in words.

1. Starting at the digit on the left, name the number in each period, followed by the period name. Do not include the period name for the ones.
2. Use commas in the number to separate the periods.

Name the number in words.

Solution

Begin with the leftmost digit, which is 8. It is in the trillions place.	eight trillion
The next period to the right is billions.	one hundred sixty-five billion
The next period to the right is millions.	four hundred thirty-two million
The next period to the right is thousands.	ninety-eight thousand
The rightmost period shows the ones.	seven hundred ten

Putting all of the words together, we write as eight trillion, one hundred sixty-five billion, four hundred thirty-two million, ninety-eight thousand, seven hundred ten.

Name each number in words:

nine trillion, two hundred fifty-eight billion, one hundred thirty-seven million, nine hundred four thousand, sixty-one

Name each number in words:

seventeen trillion, eight hundred sixty-four billion, three hundred twenty-five million, six hundred nineteen thousand, four

A student conducted research and found that the number of mobile phone users in the United States during one month in was Name that number in words.

Solution

Identify the periods associated with the number.

Name the number in each period, followed by the period name. Put the commas in to separate the periods.

Millions period: three hundred twenty-seven million

Thousands period: five hundred seventy-seven thousand

Ones period: five hundred twenty-nine

So the number of mobile phone users in the Unites States during the month of April was three hundred twenty-seven million, five hundred seventy-seven thousand, five hundred twenty-nine.

The population in a country is Name that number.

three hundred sixteen million, one hundred twenty-eight thousand, eight hundred thirty nine

One year is seconds. Name that number.

thirty one million, five hundred thirty-six thousand

Use Place Value to Write Whole Numbers

We will now reverse the process and write a number given in words as digits.

Use place value to write a whole number.

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.

Write the following numbers using digits.

• ⓐ fifty-three million, four hundred one thousand, seven hundred forty-two
• ⓑ nine billion, two hundred forty-six million, seventy-three thousand, one hundred eighty-nine

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.

Put the numbers together, including the commas. The number is

ⓑ 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.

The number is

Notice that in part ⓑ, a zero was needed as a place-holder in the hundred thousands place. Be sure to write zeros as needed to make sure that each period, except possibly the first, has three places.

Write each number in standard form:

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

53,809,051

Write each number in standard form:

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

2,022,714,466

A state budget was about 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.

So the budget was about

Write each number in standard form:

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

34,000,000 miles

Write each number in standard form:

The total weight of an aircraft carrier is million pounds.

204,000,000 pounds

Round Whole Numbers

In the U.S. Census Bureau reported the population of the state of New York as people. It might be enough to say that the population is approximately million. The word approximately means that 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. million was achieved by rounding to the millions place. Had we rounded to the one hundred thousands place, we would have as a result. Had we rounded to the ten thousands place, we would have as a result, and so on. 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 (Figure). Suppose we want to round the number to the nearest ten. Is closer to or on the number line?

Now consider the number Find in (Figure).

How do we round to the nearest ten. Find in (Figure).

The number is exactly midway between and

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

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

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

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

Let's look again at rounding to the nearest Again, we look to the ones place.

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

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
   • Yes—add 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.

Round to the nearest ten.

Round to the nearest ten:

160

Round to the nearest ten:

880

Round each number to the nearest hundred:

1. ⓐ
2. ⓑ

Round to the nearest hundred:

17,900

Round to the nearest hundred:

5,000

Round each number to the nearest thousand:

1. ⓐ
2. ⓑ

Round to the nearest thousand:

64,000

Round to the nearest thousand:

156,000

Key Concepts

• Name a whole number in words.
  1. Starting at the digit on the left, name the number in each period, followed by the period name. Do not include the period name for the ones.
  2. Use commas in the number to separate the periods.
• Use place value to write a whole number.
  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.
  3. Name the number in each period and place the digits in the correct place value position.
• 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. If yes—add 1 to the digit in the given place value. If 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.

Practice Makes Perfect

Identify Counting Numbers and Whole Numbers

In the following exercises, determine which of the following numbers are ⓐ counting numbers ⓑ whole numbers.

1. ⓐ 5, 125
2. ⓑ 0, 5, 125

1. ⓐ 50, 221
2. ⓑ 0, 50, 221

Model Whole Numbers

In the following exercises, use place value notation to find the value of the number modeled by the blocks.

561

407

Identify the Place Value of a Digit

In the following exercises, find the place value of the given digits.

1. ⓐ 9
2. ⓑ 6
3. ⓒ 0
4. ⓓ 7
5. ⓔ 5

1. ⓐ thousands
2. ⓑ hundreds
3. ⓒ tens
4. ⓓ ten thousands
5. ⓔ hundred thousands

1. ⓐ 9
2. ⓑ 3
3. ⓒ 2
4. ⓓ 8
5. ⓔ 7

1. ⓐ 8
2. ⓑ 6
3. ⓒ 4
4. ⓓ 7
5. ⓔ 0

1. ⓐ hundred thousands
2. ⓑ millions
3. ⓒ thousands
4. ⓓ tens
5. ⓔ ten thousands

1. ⓐ 8
2. ⓑ 4
3. ⓒ 2
4. ⓓ 6
5. ⓔ 7

Use Place Value to Name Whole Numbers

In the following exercises, name each number in words.

One thousand, seventy-eight

Three hundred sixty-four thousand, five hundred ten

Five million, eight hundred forty-six thousand, one hundred three

Thirty seven million, eight hundred eighty-nine thousand, five

The height of Mount Ranier is feet.

Fourteen thousand, four hundred ten

The height of Mount Adams is feet.

Seventy years is hours.

Six hundred thirteen thousand, two hundred

One year is minutes.

The U.S. Census estimate of the population of Miami-Dade county was

Two million, six hundred seventeen thousand, one hundred seventy-six

The population of Chicago was

There are projected to be college and university students in the US in five years.

Twenty three million, eight hundred sixty-seven thousand

About twelve years ago there were registered automobiles in California.

The population of China is expected to reach in

One billion, three hundred seventy-seven million, five hundred eighty-three thousand, one hundred fifty-six

The population of India is estimated at as of July

Use Place Value to Write Whole Numbers

In the following exercises, write each number as a whole number using digits.

thirty-five thousand, nine hundred seventy-five

35,975

sixty-one thousand, four hundred fifteen

eleven million, forty-four thousand, one hundred sixty-seven

11,044,167

eighteen million, one hundred two thousand, seven hundred eighty-three

three billion, two hundred twenty-six million, five hundred twelve thousand, seventeen

3,226,512,017

eleven billion, four hundred seventy-one million, thirty-six thousand, one hundred six

The population of the world was estimated to be seven billion, one hundred seventy-three million people.

7,173,000,000

The age of the solar system is estimated to be four billion, five hundred sixty-eight million years.

Lake Tahoe has a capacity of thirty-nine trillion gallons of water.

39,000,000,000,000

The federal government budget was three trillion, five hundred billion dollars.

Round Whole Numbers

In the following exercises, round to the indicated place value.

Round to the nearest ten:

1. ⓐ
2. ⓑ

1. ⓐ 390
2. ⓑ 2,930

Round to the nearest ten:

1. ⓐ
2. ⓑ

Round to the nearest hundred:

1. ⓐ
2. ⓑ

1. ⓐ 13,700
2. ⓑ 391,800

Round to the nearest hundred:

1. ⓐ
2. ⓑ

Round to the nearest ten:

1. ⓐ
2. ⓑ

1. ⓐ 1,490
2. ⓑ 1,500

Round to the nearest thousand:

1. ⓐ
2. ⓑ

Round to the nearest hundred:

1. ⓐ
2. ⓑ

Round to the nearest thousand:

1. ⓐ
2. ⓑ

Everyday Math

Writing a Check Jorge bought a car for He paid for the car with a check. Write the purchase price in words.

Twenty four thousand, four hundred ninety-three dollars

Writing a Check Marissa's kitchen remodeling cost She wrote a check to the contractor. Write the amount paid in words.

Buying a Car Jorge bought a car for Round the price to the nearest:

1. ⓐ ten dollars
2. ⓑ hundred dollars
3. ⓒ thousand dollars
4. ⓓ ten-thousand dollars

1. ⓐ ?24,490
2. ⓑ ?24,500
3. ⓒ ?24,000
4. ⓓ ?20,000

Remodeling a Kitchen Marissa's kitchen remodeling cost Round the cost to the nearest:

1. ⓐ ten dollars
2. ⓑ hundred dollars
3. ⓒ thousand dollars
4. ⓓ ten-thousand dollars

Population The population of China was in Round the population to the nearest:

1. ⓐ billion people
2. ⓑ hundred-million people
3. ⓒ million people

Astronomy The average distance between Earth and the sun is kilometers. Round the distance to the nearest:

1. ⓐ hundred-million kilometers
2. ⓑ ten-million kilometers
3. ⓒ million kilometers

Writing Exercises

In your own words, explain the difference between the counting numbers and the whole numbers.

Answers may vary. The whole numbers are the counting numbers with the inclusion of zero.

Give an example from your everyday life where it helps to round numbers.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ If most of your checks were…

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don't get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

Glossary

coordinate

A number paired with a point on a number line is called the coordinate of the point.

counting numbers

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

number line

A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left.

origin

The origin is the point labeled 0 on a number line.

place value system

Our number system is called a place value system because the value of a digit depends on its position, or place, in a number.

rounding

The process of approximating a number is called rounding.

whole numbers

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

What Is the Next Whole Number After One Hundred Thousand

Source: https://opentextbc.ca/prealgebraopenstax/chapter/introduction-to-whole-numbers/

Share this post