Place Value
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 ...
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.
The figure below shows how the number \(5,278,194\) is written in a place value chart.
Image credit: OpenStax Prealgebra
- 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
In the number \(63,407,218;\) find the place value of each of the following digits:
- \(7\)
- \(0\)
- \(1\)
- \(6\)
- \(3\)
Solution
Write the number in a place value chart, starting at the right.
Image credit: OpenStax Prealgebra
- The \(7\) is in the thousands place.
- The \(0\) is in the ten thousands place.
- The \(1\) is in the tens place.
- The \(6\) is in the ten millions place.
- The \(3\) is in the millions place.
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.
Image credit: OpenStax Prealgebra
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.
Naming a Whole Number in Words
- 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.
- Use commas in the number to separate the periods.
Example
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 |
Image credit: OpenStax Prealgebra
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.
Example
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.
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.
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
- Identify the words that indicate periods. (Remember the ones period is never named.)
- Draw three blanks to indicate the number of places needed in each period. Separate the periods by commas.
- Name the number in each period and place the digits in the correct place value position.
Example
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
a. 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 \(53,401,742.\)
b. 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 \(9,246,073,189.\)
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.
Example
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.
So the budget was about \($77,000,000,000.\)
Video Summary: Determining Place Value
Video credit: Mathispower4u
This lesson is part of:
Introducing Numbers