Representing Numbers: Standard Form, Word Form, and Expanded Form

One way to help understand place value is by writing numbers in standard form, word form, and expanded form. For example, 9 in 129 has a different value than the 9 in 192. Knowing how to represent numbers in these three different ways will help build place value concepts. 

What are these three forms of writing numbers? 

Standard form is the usual way of writing numbers. One example is 756. This is how we see numbers everyday in the grocery, on our phones, computers, etc. 

Expanded form is breaking down the numbers in such a way that you see the value of each number. So, the expanded form of 756 is 700 + 50 + 6. 

Word form is when you write a number the way that you read it. When you see the number 756, you write it as “seven hundred fifty-six”. 

How do you write numbers in standard form to word form?

When writing numbers from standard form to word form, having a place value chart will be very helpful. A place value chart shows how each digit in a number is related. It helps you read and separate the values into groups of three especially with big numbers. 

Place value chart from ones to hundred millions

Just look at this number 612,321,589. This number is read as “six hundred twelve million, three hundred twenty-one thousand, five hundred eighty-nine”. Notice that for each group of three, there is a comma or sometimes a space. These commas or spaces are not just for ease of reading. Commas also indicate the period or the group of digits in your number.

How do you write numbers in standard form to expanded form?

When writing numbers in expanded form, you will also find a place value chart helpful. Place value chart not just shows how the numbers are grouped, but also shows that each digit in a number increases by a power of ten from right to left. This will help decompose a number so that your students will know that having a 9 in the tens place has a different value than having a 9 in the hundreds place. 

Here’s a place value chart showing the value of a number.

Place value chart

When the number 721,345,698 is placed in a place value chart, you will see the following: 

  • 7 is in the hundred millions place and has a value of 700,000,000
  • 2 is in the ten millions place and has a value of 20,000,000
  • 1 is in the millions place and has a value of 1,000,000
  • 3 is in the hundred thousands place and has a value of 300,000
  • 4 is the ten thousands place and has a value of 40,000
  • 5 is in the thousands place and has a value of 5,000
  • 6 is in the hundreds place and has a value of 600
  • 9 is in the tens place and has a value of 90
  • 8 is in the ones place and has a value of 8

When you put them all together, you will have a number written in expanded form. So 721,345,698 written in expanded form is 700,000,000 + 20,000,000 + 1,000,000 + 300,000 + 40,000 + 5,000 + 600 + 90 + 8.

To start practicing converting numbers into their different forms, you can try our Match the Numbers worksheet. This activity asks the students to match the standard, expanded, and word forms of each number. This is a cut-and-paste activity but is easily convertible to just a pen-and-paper activity. An answer key is included on the second page.

Standard Form, Word Form, Expanded Form Activity

Need a more comprehensive worksheet on reading and writing numbers? Check out these activities on Teachers Pay Teachers.

Using base-ten blocks is another good tool to help decompose a number in expanded form. You can start with our Place Value with Base-ten Blocks activity.