1.1: Place Value and Names for Whole Numbers (2024)

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    Learning Objectives
    • 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: \(1, 2, 3, 4, 5, …\) 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.

    Definition: Counting Numbers

    The counting numbers start with \(1\) and continue.

    \(1, 2, 3, 4, 5 \ldots \)

    Counting numbers and whole numbers can be visualized on a number line as shown in Figure \(\PageIndex{1}\).

    1.1: Place Value and Names for Whole Numbers (2)

    Figure \(\PageIndex{1}\): The numbers on the number line increase from left to right, and decrease from right to left.

    The point labeled \(0\) is called the origin. The points are equally spaced to the right of 0 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.

    Definition: Whole Numbers

    The whole numbers are the counting numbers and zero.

    \(0, 1, 2, 3, 4, 5 \ldots\)

    We stopped at \(5\) 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.

    Example \(\PageIndex{1}\): Number Identification

    Which of the following are

    1. counting numbers
    2. whole numbers

    \[0, \dfrac{1}{4}, 3, 5.2, 15, 105 \nonumber\]

    Solution

    1. The counting numbers start at \(1\), so \(0\) is not a counting number. The numbers \(3\), \(15\), and \(105\) are all counting numbers.
    2. Whole numbers are counting numbers and \(0\). The numbers \(0, 3, 15,\) and \(105\) are whole numbers. The numbers \(\dfrac{1}{4}\) and \(5.2\) are neither counting numbers nor whole numbers. We will discuss these numbers later.
    Exercise \(\PageIndex{1}\)

    Which of the following are

    1. whole numbers

    \[0, \dfrac{2}{3}, 2, 9, 11.8, 241, 376 \nonumber \]

    Answer a

    \(2, 9, 241, 376\)

    Answer b

    \(0, 2, 9, 241, 376\)

    Exercise \(\PageIndex{2}\)

    Which of the following are

    1. counting numbers
    2. whole numbers

    \[0, \dfrac{5}{3}, 7, 8.8, 13, 201 \nonumber \]

    Answer a

    \(7, 13, 201\)

    Answer b

    \(0, 7, 13, 201\)

    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 \(537\) has a different value than the number \(735\). Even though they use the same digits, their value is different because of the different placement of the \(3\) and the \(7\) and the \(5\).

    Money gives us a familiar model of place value. Suppose a wallet contains three \($100\) bills, seven \($10\) bills, and four \($1\) bills. The amounts are summarized in Figure \(\PageIndex{2}\). How much money is in the wallet?

    1.1: Place Value and Names for Whole Numbers (3)

    Figure \(\PageIndex{2}\)

    Find the total value of each kind of bill, and then add to find the total. The wallet contains \($374\).

    1.1: Place Value and Names for Whole Numbers (4)

    Base-\(10\) blocks provide another way to model place value, as shown in Figure \(\PageIndex{3}\). The blocks can be used to represent hundreds, tens, and ones. Notice that the tens rod is made up of \(10\) ones, and the hundreds square is made of \(10\) tens, or \(100\) ones.

    1.1: Place Value and Names for Whole Numbers (5)

    Figure \(\PageIndex{3}\)

    Figure \(\PageIndex{4}\) shows the number \(138\) modeled with base-\(10\) blocks.

    1.1: Place Value and Names for Whole Numbers (6)

    Figure \(\PageIndex{4}\): We use place value notation to show the value of the number 138.

    1.1: Place Value and Names for Whole Numbers (7)

    Digit Place value Number Value Total value
    1 hundreds 1 100 100
    3 tens 3 10 30
    8 ones 8 1 +8
    Sum = 138
    Example \(\PageIndex{2}\): place value notation

    Use place value notation to find the value of the number modeled by the base-\(10\) blocks shown.

    1.1: Place Value and Names for Whole Numbers (8)

    Figure \(\PageIndex{5}\)

    Solution

    There are \(2\) hundreds squares, which is \(200\).

    There is \(1\) tens rod, which is \(10\).

    There are \(5\) ones blocks, which is \(5\).

    1.1: Place Value and Names for Whole Numbers (9)

    Digit Place value Number Value Total value
    2 hundreds 2 100 200
    1 tens 1 10 10
    5 ones 5 1 +5
    215

    The base-\(10\) blocks model the number \(215\).

    Identify the Place Value of a Digit

    By looking at money and base-10 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 base-\(10\) 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 \(\PageIndex{8}\) shows how the number \(5,278,194\) is written in a place value chart.

    1.1: Place Value and Names for Whole Numbers (10)

    Figure \(\PageIndex{8}\)

    • The digit \(5\) is in the millions place. Its value is \(5,000,000\).
    • The digit \(2\) is in the hundred thousands place. Its value is \(200,000\).
    • The digit \(7\) is in the ten thousands place. Its value is \(70,000\).
    • The digit \(8\) is in the thousands place. Its value is \(8,000\).
    • The digit \(1\) is in the hundreds place. Its value is \(100\).
    • The digit \(9\) is in the tens place. Its value is \(90\).
    • The digit \(4\) is in the ones place. Its value is \(4\).
    Example \(\PageIndex{3}\): place value

    In the number \(63,407,218\); find the place value of each of the following digits:

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

    Solution

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

    1.1: Place Value and Names for Whole Numbers (11)

    Figure \(\PageIndex{9}\)

    1. The \(7\) is in the thousands place.
    2. The \(0\) is in the ten thousands place.
    3. The \(1\) is in the tens place.
    4. The \(6\) is in the ten millions place.
    5. The \(3\) is in the millions place.
    Exercise \(\PageIndex{6}\)

    For each number, find the place value of digits listed: \(519,711,641,328\)

    1. \(9\)
    2. \(4\)
    3. \(2\)
    4. \(6\)
    5. \(7\)
    Answer a

    billions

    Answer b

    ten thousands

    Answer c

    tens

    Answer d

    hundred thousands

    Answer e

    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.

    1.1: Place Value and Names for Whole Numbers (12)

    So the number \(37,519,248\) 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.

    How to: Name a Whole Number in Words.

    Step 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.

    Step 2. Use commas in the number to separate the periods.

    Example \(\PageIndex{4}\): name whole numbers

    Name the number \(8,165,432,098,710\) 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

    1.1: Place Value and Names for Whole Numbers (13)

    Putting all of the words together, we write \(8,165,432,098,710\) as eight trillion, one hundred sixty-five billion, four hundred thirty-two million, ninety-eight thousand, seven hundred ten.

    Exercise \(\PageIndex{7}\)

    Name each number in words: \(9,258,137,904,061\)

    Answer

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

    Example \(\PageIndex{5}\): name whole numbers

    A student conducted research and found that the number of mobile phone users in the United States during one month in 2014 was \(327,577,529\). Name that number in words.

    Solution

    Identify the periods associated with the number.

    1.1: Place Value and Names for Whole Numbers (14)

    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.

    Exercise \(\PageIndex{9}\)

    The population in a country is \(316,128,839\). Name that number

    Answer

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

    Use Place Value to Write Whole Numbers

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

    How to: Use Place Value to Write Whole Numbers

    Step 1. Identify the words that indicate periods. (Remember the ones period is never named.)

    Step 2. Draw three blanks to indicate the number of places needed in each period. Separate the periods by commas.

    Step 3. Name the number in each period and place the digits in the correct place value position.

    Example \(\PageIndex{6}\): write whole numbers

    Write the following numbers using digits.

    1. fifty-three million, four hundred one thousand, seven hundred forty-two
    2. nine billion, two hundred forty-six million, seventy-three thousand, one hundred eighty-nine

    Solution

    1. 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.

    1.1: Place Value and Names for Whole Numbers (15)

    Put the numbers together, including the commas. The number is \(53,401,742\).

    1. 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.

    1.1: Place Value and Names for Whole Numbers (16)

    The number is \(9,246,073,189.\)

    Notice that in part (b), 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.

    Exercise \(\PageIndex{11}\)

    Write each number in standard form:

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

    Answer

    \(53,809,051\)

    Exercise \(\PageIndex{12}\)

    Write each number in standard form:

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

    Answer

    \(2,022,714,466\)

    Example \(\PageIndex{7}\): write standard form

    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.

    1.1: Place Value and Names for Whole Numbers (17)

    So the budget was about \($77,000,000,000\).

    Exercise \(\PageIndex{14}\)

    Write each number in standard form:

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

    Answer

    \(204,000,000\: pounds\)

    Contributors and Attributions

    1.1: Place Value and Names for Whole Numbers (2024)

    FAQs

    Is 1.1 a whole number? ›

    Examples: 0, 7, 212 and 1023 are all whole numbers

    (But numbers like ½, 1.1 and −5 are not whole numbers.)

    What are the names and place values of whole numbers? ›

    The first digit starting from the left is the units or ones place value. The second digit from the left is the tens place value. The third digit from the left is the hundreds place value. The fourth digit from the left is the thousands place value.

    What is the place value and place name? ›

    Hint: As we know place name is the position of digit in the number like ones, tens, hundreds, thousands and so on. Also, the place value of a digit is the value of its position multiplied by the digit itself.

    What is the place value of 1? ›

    Solution
    DigitPlace valueNumber
    2hundreds2
    1tens1
    5ones5
    1 more row
    Nov 27, 2023

    What is 1.1 as a number? ›

    1.1 is read as One and one tenths, the One is the whole number, the 1 is the numerator, and the denominator is the 10.

    What is 1.1 rounded to the nearest whole number? ›

    If we round off the number 1.1 to the nearest one then we'll be getting 1.

    What are names for whole numbers? ›

    Synonyms of whole numbers
    • numbers.
    • digits.
    • figures.
    • numerals.
    • symbols.
    • integers.
    • numerics.
    • fractions.

    What is an example of a place value and value? ›

    In math, place values refer to the meaning of each digit in a number. For example, 35 has 2 digits, 3 and 5. The 3 is in the tens place and its value is 30. The 5 is in the ones place and its value is 5.

    What is a whole number value? ›

    A whole number is any positive number that does not include a fractional or decimal part, and zero. Examples: 0, 1, 2, 3, 4, 5, 6, and 7. Non-examples: 3, 2.7, or 3 ½

    What are the number names place value chart? ›

    Difference Between Place Value and Face Value
    DigitsPlace ValueFace Value
    2Thousands2
    4Hundreds4
    5Tens5
    6Units or ones6

    How do I write place value? ›

    In math, every digit in a number has a place value. Place value can be defined as the value represented by a digit in a number on the basis of its position in the number. For example, the place value of 7 in 3,743 is 7 hundred or 700. However, the place value of 7 in 7,432 is 7 thousand or 7,000.

    What is the place value of a whole number? ›

    Place value is the value of the digit in its position. For example, the number 358 has three columns or “places,” each with a specific value. In 358, the 3 is in the “hundreds” place, the 5 is in the “tens” place, and the 8 is in the “ones” place.

    What are the number places names? ›

    Before the decimal, in order from left to right (starting with billions), there are the following place values: billions, hundred millions, ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones. The decimal falls to the right of the ones place.

    What is a value of 1? ›

    Value
    DigitsPlace ValueValue
    9tens or 10s90
    1ones or 1s1
    2tenths or 0.1s0.2
    3hundredths or 0.01s0.3
    5 more rows

    Is 1.1 a rational number? ›

    Do you know 1.1 is a rational number? Yes, it is because 1.1 can be written as 1.1= 11/10. Now let us talk about non-terminating decimals such as 0.333..... Since 0.333... can be written as 1/3, therefore it is a rational number.

    Can 1 1 be a whole number? ›

    A whole number is any positive number that does not include a fractional or decimal part, and zero. Can we write 1/2 as a whole number? No, we cannot write the given fraction as a whole number. Whole numbers do not include fractional or decimal numbers.

    Is 1.1 a natural number? ›

    For example, no natural number exists between 1 and 2, as 1.1, 1.2, 1.3, 1.7, 1.9, etc. are decimal numbers.

    Is 1.1 an integer? ›

    An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .09, and 5,643.1.

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