Place Value and Names for Whole Numbers
Learning Objective(s)
· Find the place value of a digit in a whole number.
· Write a whole number in words and in standard form.
· Write a whole number in expanded form.
Introduction
Mathematics involves solving problems that involve numbers. We will work with whole numbers, which are any of the numbers 0, 1, 2, 3, and so on. We first need to have a thorough understanding of the number system we use. Suppose the scientists preparing a lunar command module know it has to travel 382,564 kilometers to get to the moon. How well would they do if they didn’t understand this number? Would it make more of a difference if the 8 was off by 1 or if the 4 was off by 1?
In this section, you will take a look at digits and place value. You will also learn how to write whole numbers in words, standard form, and expanded form based on the place values of their digits.
A digit is one of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. All numbers are made up of one or more digits. Numbers such as 2 have one digit, whereas numbers such as 89 have two digits. To understand what a number really means, you need to understand what the digits represent in a given number.
The position of each digit in a number tells its value, or place value. We can use a placevalue chart like the one below to easily see the place value for each digit. The place values for the digits in 1,456 are shown in this chart.
PlaceValue Chart  
Trillions  Billions  Millions  Thousands  Ones  










 1  4  5  6 
Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones 
In the number 1,456, the digit 1 is in the thousands place. The digit 4 is in the hundreds place. The digit 5 is in the tens place, and the digit 6 is in the ones place.
As you see above, you can tell a digit’s value by looking at its position. Look at the number of digits to the right of the digit, or write your number into a placevalue chart, with the last digit in the ones column. Both these methods are shown in the example below.
Example  
Problem  The development of a city over the past twenty years cost $962,234,532,274,312. What is the value of the digit 6 in this number?  
 Write the number in the placevalue chart. Read the value of the 6 from the chart.  
$962,234,532,274,312 60,000,000,000,000 
 
Answer The value of the digit 6 is 60 trillion. 
 
In a far away galaxy, there are 2,968,351,472 stars. What does the digit 3 represent in this problem?
A) three hundred thousands
B) three hundreds
C) three hundred trillions
D) three hundred millions

The standard form of a number refers to a type of notation in which digits are separated into groups of three by commas. These groups of three digits are known as periods. For example, 893,450,243 has three periods with three digits in each period, as shown below.
PlaceValue Chart  
Trillions  Billions  Millions  Thousands  Ones  





 8  9  3  4  5  0  2  4  3 
Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones 
Let’s examine the number of digits and periods in a greater number. The number of body cells in an average adult human is about one hundred trillion. This number is written as 100,000,000,000,000. Notice that there are 15 digits and 5 periods. Here is how the number would look in a placevalue chart.
PlaceValue Chart  
Trillions  Billions  Millions  Thousands  Ones  
1  0  0  0  0  0  0  0  0  0  0  0  0  0  0 
Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones 
You are now familiar with the place values of greater numbers, so let’s examine a problem that involves converting from standard form to a word name.
Converting Standard Form to Word Names
We often use word names to write numbers. A word name for 42 is “fortytwo.” The total number of weeks in a year, 52, is written as “fiftytwo.”
For whole numbers with three digits, use the word “hundred” to describe how many hundreds there are in the number. For example, for the number of days in a normal year, 365, the digit 3 is in the hundreds place. The word name for the number is “three hundred sixtyfive.”
For whole numbers with four digits, begin the name with the number of thousands, followed by the period name, as in the example below.
Example  
Problem  A man owes $2,562 on a car. Write the word name for this.  
 
Answer  The word name is two thousand, five hundred sixtytwo.  
For word names of greater numbers, begin at the left with the greatest period. For each period, write the one to threedigit number in the period, and then the period name. See the example below.
Example  
Problem  The construction of a new athletic center cost $23,456,390. Write the word name for this number.  
 
Answer  The word name is twentythree million, four hundred fiftysix thousand, three hundred ninety.  
Converting Word Names to Standard Form
When converting word names to standard form, the word “thousand” tells you which period the digits are in. See the example below.
Example  
Problem  Fortyseven thousand, five hundred eightysix blueberries are produced on a farm over the course of three years. Write this number in standard form.  
Fortyseven thousand
Five hundred eightysix
Standard Notation is 47,586
 
Answer  The number in standard form is 47,586.  
Below is an example with a number containing more digits. The words “million” and “thousand” tell you which periods the digits are in. The periods are separated by commas.
Example  
Problem  There are three hundred eight million, six hundred thirtytwo thousand, nine hundred seventyeight bacteria in a sample of soil. Write this number in standard form.  
 
Answer  The number in standard form is 308,632,978.  
Some numbers in word form may not mention a specific period. For example, three million, one hundred twelve written in standard form is 3,000,112. Because the thousands period is not mentioned, you would write three zeros in the thousands period. You can use a placevalue chart to make it easier to see the values of the digits. See the example below.
Example 
 
Problem  A company had a new office building constructed. The final cost was seventyfour million, three hundred sixtytwo dollars. Write this number in standard form.  

Placing this number in a place value chart shows that the thousands period is zero.
Remember to separate each period with a comma.  
Answer The number written in standard form is $74,000,362.  
Sometimes it is useful to write numbers in expanded form. In expanded form, the number is written as a sum of the value of each digit.
Example  
Problem  During the week, Mike drives a total of 264 miles. Write 264 in expanded form.  
First, identify the value of each digit.
In numerical form:  
264  200  
264  60  
264  4  
In word form: 
 
264  2 hundreds  
264  6 tens  
264  4 ones  
Then, write the numbers as a sum.  
Answer  264 written in expanded form is
200 + 60 + 4, or
2 hundreds + 6 tens + 4 ones, or
(2 • 100) + (6 • 10) + (4 • 1)  
You can also use a placevalue chart to help write a number in expanded form. Suppose the number of cars and pickup trucks in the U.S. at this very moment is 251,834,697. Place this number in a placevalue chart.
PlaceValue Chart  
Trillions  Billions  Millions  Thousands  Ones  





 2  5  1  8  3  4  6  9  7 
Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones  Hundreds  Tens  Ones 
2 hundred millions  200,000,000 
+ 5 ten millions  +50,000,000 
+ 1 million  +1,000,000 
+ 8 hundred thousands  +800,000 
+ 3 ten thousands  +30,000 
+ 4 thousands  +4,000 
+ 6 hundreds  +600 
+ 9 tens  +90 
+ 7 ones  +7 
Summary
Whole numbers that are greater than 9 consist of multiple digits. Each digit in a given number has a place value. To better understand place value, numbers can be put in a placevalue chart so that the value of each digit can be identified. Numbers with more than three digits can be separated into groups of three digits, known as periods. Any whole number can be expressed in standard form, expanded form, or as a word name.