Standard, Expanded, and Word Form - Third Grade Mathematics

Numbers can be shown in several different ways depending on what we want to communicate. In this chapter, you will learn the three essential forms of every whole number: standard form, expanded form, and word form. Mastering these three formats will give you a crystal-clear picture of what numbers really mean and how their individual place values work together.

The Three Ways to Write a Number

Whenever you encounter a number, you can write it using regular digits, stretched out by its place values, or spelled out in words.

+---------------+---------------------------------------+---------------------+
|     Form      | What It Looks Like                    | Purpose             |
+---------------+---------------------------------------+---------------------+
| Standard Form | 4,528                                 | Quick, everyday use |
| Expanded Form | 4,000 + 500 + 20 + 8                  | Shows value of each |
| Word Form     | four thousand, five hundred twenty-eight | Spoken and written |
+---------------+---------------------------------------+---------------------+

Standard Form

Standard form is the way you usually see numbers written in books, on clocks, and in grocery stores. It uses only digits and commas.
- Examples: 342; 1,805; 7,429; 10,000.


When writing standard form, remember to place a comma between the thousands digit and the hundreds digit for numbers with 4 or more digits.

Expanded Form

Expanded form stretches a number out like a rubber band to reveal the exact value contributed by each digit. You write the number as an addition sentence showing the value of each place.

Standard Form: 6,347

Breakdown:
6 Thousands  =  6,000
3 Hundreds   =    300
4 Tens       =     40
7 Ones       =      7

Expanded Form: 6,000 + 300 + 40 + 7

What happens when a digit is 0? For the number 5,082:
- 5 thousands = 5,000

- 0 hundreds = 0

- 8 tens = 80

- 2 ones = 2


You can write expanded form as either: 5,000 + 0 + 80 + 2 or simply: 5,000 + 80 + 2

Both expressions are completely correct, but leaving out the 0 is more common because adding 0 does not change the total value.

Word Form

Word form expresses the number using English words, exactly the way you say it out loud.

Here are the key rules for spelling numbers correctly:
- Read the thousands period first, say the word "thousand", and place a comma: "six thousand,"

- Read the remaining three digits together: "three hundred forty-seven"

- Use a hyphen (-) for two-digit numbers between 21 and 99 that do not end in zero (such as twenty-one, forty-seven, seventy-eight, ninety-nine).

- Do not say or write the word "and" when reading whole numbers! In mathematics, the word "and" is reserved for decimal points, which you will study in later grades. Say "four hundred five", not "four hundred and five".


Converting Between Forms

Being able to switch smoothly between standard, expanded, and word form is a core mathematical skill.

From Expanded Form to Standard Form

Look at: 8,000 + 600 + 9 Notice that there are no tens in this expression! When writing in standard form, you must place a 0 in the empty tens column:
- Thousands: 8

- Hundreds: 6

- Tens: 0

- Ones: 9
Standard form: 8,609.

If you forgot the zero and wrote 869, you would have only eight hundred sixty-nine, which is missing over seven thousand units!

From Word Form to Standard Form

Consider: "seven thousand, forty-two"
- Break it into parts: "seven thousand" -> 7 in the thousands place.

- Look for hundreds: the phrase does not mention any hundreds, so place a 0 in the hundreds place.

- Look for tens and ones: "forty-two" -> 4 in the tens place, 2 in the ones place.
Standard form: 7,042.

Step-by-Step Summary Table

+---------------+---------------------+--------------------------------------------+
| Standard Form | Expanded Form       | Word Form                                  |
+---------------+---------------------+--------------------------------------------+
| 3,214         | 3,000 + 200 + 10 + 4| three thousand, two hundred fourteen       |
| 5,608         | 5,000 + 600 + 8     | five thousand, six hundred eight           |
| 9,070         | 9,000 + 70          | nine thousand, seventy                     |
| 10,000        | 10,000              | ten thousand                               |
+---------------+---------------------+--------------------------------------------+

Chapter Practice Exercises

Practice converting between standard, expanded, and word form with these questions.

  1. Write each number in expanded form: a. 2,754 b. 6,081 c. 8,920 d. 4,005
  2. Write each number in standard form: a. 5,000 + 300 + 60 + 2 b. 7,000 + 400 + 9 c. 9,000 + 80 d. 1,000 + 500 + 30
  3. Write each number in word form: a. 4,329 b. 7,015 c. 3,800 d. 6,004
  4. Write in standard form: "eight thousand, two hundred sixty-one".
  5. Write in standard form: "five thousand, seventy-three".
  6. A hiker climbed a mountain that is 4,209 feet tall. Write this elevation in expanded form and in word form.

Solutions and Step-by-Step Answers

  1. Expanded form: a. 2,754 = 2,000 + 700 + 50 + 4 b. 6,081 = 6,000 + 80 + 1 (or 6,000 + 0 + 80 + 1) c. 8,920 = 8,000 + 900 + 20 d. 4,005 = 4,000 + 5
  2. Standard form: a. 5,000 + 300 + 60 + 2 = 5,362 b. 7,000 + 400 + 9 = 7,409 (0 tens) c. 9,000 + 80 = 9,080 (0 hundreds and 0 ones) d. 1,000 + 500 + 30 = 1,530 (0 ones)
  3. Word form: a. 4,329 = four thousand, three hundred twenty-nine b. 7,015 = seven thousand, fifteen c. 3,800 = three thousand, eight hundred d. 6,004 = six thousand, four
  4. "Eight thousand, two hundred sixty-one" in standard form is 8,261.
  5. "Five thousand, seventy-three" has 5 thousands, 0 hundreds, 7 tens, and 3 ones, which is 5,073.
  6. For 4,209 feet:
  7. Expanded form: 4,000 + 200 + 9 feet
  8. Word form: four thousand, two hundred nine feet