K-12 – Standard, Expanded and Word Form

What Is the Difference Between Expanded Form and Standard Form?

The standard form is the combination of digits written together as a single number. In the expanded form the digits of the number are split into each of the individual digits with their place value and written in expanded form. The example of standard form of a number is 4,982 and the same number can be written in expanded form as 4 × 1000 + 9 × 100 + 8 × 10 + 2 × 1 = 4000 + 900 + 80 + 2. [1]

Standard

A standard form is a form of writing a given mathematical concept like an equation, number, or an expression in a form that follows certain rules. Representing very large or very small numbers concisely, the standard form is used. For example, 4.5 billion years is written as 4,500,000,000 years. As you can see here, writing a large number like 4.5 billion in its number form is not just ambiguous but also time-consuming and there are chances that we may write a few 0’s less or more while writing in the number form. In this case, writing the number in standard form is very helpful. For example, the standard form of 4,500,000,000 = 4.5 × 10⁹. Not only numbers but the fractions, equations, expressions, polynomials, etc., also can be written in the standard form. [2]

To write numbers in standard form, we follow a simple process. We identify the number between 1 and 10 and then determine how many times we need to multiply it by 10 to get the original number. Let’s take the number 5,000 as an example. We can write it in standard form as 5 x 10^3. The number 5 is between 1 and 10, and we multiply it by 10 three times to get 5,000. [3]

Expanded

The expanded form helps us to better understand a given number in maths. Let us take an example of the number 875294831. It is difficult to understand this number. Here an expanded form helps us to understand each of the digits based on their place value. Let us take a simple number 324 and try to find its expanded form. 324 is written in expanded form as 300 + 20 + 4. It means there are three hundred, two tens, and 4 ones in this number. We can easily understand the meaning of each digit of a number through its expanded form.

Trying to learn a number with a higher number of digits is very difficult without knowing how to express it in expanded form. The expanded form helps us to know the building blocks of higher numbers. Each of the digits can be written in the multiple forms of 1, 10, 100, 1000.

Expanded Form in Maths: Here are the below steps, which you can follow to write the expanded form: [1]

Get the number in its standard form.
Determine its place values using the place value chart.
Multiply the number by its place value.
Show it as, digit × place value.
Represent all the digits as the product of the digit and its place value.

Word

Numbers in words means expressing the given numerals in words or spellings. For example, the number 1000 in words is written as one thousand. We can represent all natural numbers in words on the basis of the place value of their digits, such as ones, tens, hundreds, thousands, and so on.

What are Number Names?

When numbers are expressed in words, we call them number names. Number names help us to learn and identify numbers easily.

For example, 1 can be written and read in words as one, therefore, the number name for 1 is one.
2 is written and read in words as two.
3 is written in words as three.
4 is written and read in words as four.
5 is written and read in words as five.
6 is written and read in words as six.
7 is written and read in words as seven.
8 is written and read in words as eight.
9 is written and read in words as nine.
10 is written and read in words as ten.

With the help of number names from one to ten, we can write and read higher-value numbers in words.

Tips to Learn Number Names

The following tips can be kept in mind to write numbers in words:

The number names from 1 to 10 can be written directly because each number name is unique, as 1- one, 2-two, 3-three, and so on.
The number names from 11 to 20 can also be written directly because each number name is unique, as 11 – eleven, 12-twelve, and so on.
The numbers and spellings of the multiples of 10 can be written as 20- twenty, 30- thirty, 40- forty, 50- fifty, 60- sixty, 70- seventy, 80- eighty, 90- ninety.
Now, after 20, starting from 21, we follow a different rule. The word form of 20 and 1 can be combined to write 21 as twenty-one, 22 as twenty-two, and so on. Similarly, we can write number names for 31, 41, 51, and so on.
For large numbers write the number and their word form, like 100 – hundred, 1000 – thousand, and so on.
The number 101 in words is written as one hundred one and 1001 is written as one thousand one and so on.

Observe the pattern which will help to write and read higher value numbers in words. [4]

100 – Hundred
200 – Two-Hundred
300 – Three-Hundred
400 – Four-Hundred
500 – Five-Hundred
600 – Six-Hundred
700 – Seven-Hundred
800 – Eight-Hundred
900 – Nine-Hundred
1000 – One-Thousand or Thousand

Similarly,

2000 – Two thousand
5000 – Five thousand
10,000 – Ten Thousand
15,000 – Fifteen Thousand
16,000 – Sixteen thousand
20,000 – Twenty Thousand
25,000 – Twenty-Five Thousand
30,000 – Thirty Thousand
35,000 – Thirty-Five Thousand
40, 000 – Forty Thousand
45,000 – Forty-Five Thousand
100,000 – One hundred thousand
200, 000 – Two hundred thousand
300, 000 – Three hundred thousand
400, 000 – Four hundred thousand
500, 000 – Five hundred thousand

Example

Write the number names for the following numbers:

8936
9000.

Solution

8936 – Eight thousand nine hundred thirty-six.
9000 – Nine thousand.

References

[1] “Expanded Form – Meaning, Decimals in Expanded Form, Examples.” 2023. CUEMATH. Accessed December 28. https://www.cuemath.com/numbers/expanded-form/.

[2] “Standard Form – Equations, Examples: Standard Form in Math.” 2023. CUEMATH. Accessed December 28. https://www.cuemath.com/algebra/standard-form/.

[3] Hart, Lucy. 2023. “What Is Standard Form?” DoodleLearning. December 19. https://doodlelearning.com/us/math/skills/numbers/standard-form.

[4] “Numbers in Words – Number Names 1 to 100: One to Hundred Spelling.” 2023. CUEMATH. Accessed December 28. https://www.cuemath.com/numbers/number-names/.

Additional Reading

⭐ Hart, Lucy. 2023. “How to Write Numbers in Words.” DoodleLearning. December 19. https://doodlelearning.com/us/math/skills/numbers/word-form.

“Numbers – Definition, Types of Numbers: What Are Numbers?” 2023. CUEMATH. Accessed December 28. https://www.cuemath.com/numbers/.

“Number Names 1 to 1000 – Spelling: Numbers in Words 1 to 1000.” 2023. CUEMATH. Accessed December 28. https://www.cuemath.com/numbers/number-names-1-to-1000/.

⭐ “Representation of Numbers in Different Forms (Standard, Word, Place Value, Visual, Expanded) – BYJUS.” 2022. BYJU’S. September 15. https://byjus.com/us/math/the-different-forms-of-representing-numbers/.

⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.

The featured image on this page is from the YouTube video Whole Number Expanded Form, Word Form, and Standard Form | Math with Mr. J.