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. Now with this understanding, let us move ahead to know more about the expanded form.
| 1. | What is the Meaning of Expanded Form? |
| 2. | Writing numbers in Expanded Form |
| 3. | Decimals in Expanded Form |
| 4. | FAQs on Expanded Form |
The way the whole numbers are formed well defines the number. The value of each digit in mathematics can be written in expanded form. Showing the number as a sum of each digit multiplied by its place value is the expanded form of a number. Let us look at the example of expanded form 1,278 = 1,000 + 200 + 70 + 8.
Expanded form is useful to split and present the higher digit number in its units, tens, hundreds, thousands form. An expanded form helps to better understand and rightly read the higher digit numbers. A number of the form 10030, is sometimes difficult to understand directly and can be represented in expanded form as 10030 = 10,000 + 30.
Some more examples of the expanded form are provided in the following table.
| Number | Ten Thousand | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|
| 452 | 4 | 5 | 2 | ||
| 605 | 6 | 0 | 5 | ||
| 3854 | 3 | 8 | 5 | 4 | |
| 40980 | 4 | 0 | 9 | 8 | 0 |
The expansion of a number is the separation of numbers based on place values. This is the intermediate step that helps us understand how the number has to be read. The expanded form helps us to know the place value of each digit within a number. Further, there are three different ways to write numbers in expanded form. The number 4537 can be written in one way of expanded form as 4531 = 4000 + 500 + 30 + 7, in the second way as 4531 = 4 × 1000 + 5 × 100 + 3 × 10 + 7 × 1, and in the third way as 4537 = 4 × thousands + 5 × hundreds + 3 × tens + 7 × ones.
Expanded Form in Maths: Here are the below steps, which you can follow to write the expanded form:
Any number we get to read is decomposed. This process is called expanding the number. After decomposing in the expanded form we interpret the number in its standard form. The following points help us to understand more about expanded form.
Unlike whole numbers, decimal numbers can also be written in the expanded form. For writing the decimals in expanded form, we multiply each of the decimal digits with increasing exponent values of (1/10). Let us try to understand this with the help of a simple example of a decimal number. The decimal number 0.437 can be written in expanded form as 4 × (1/10) + 3 × (1/10) 2 + 7 × (1/10) 3 = 4 × (1/10) + 3 × (1/100) + 7 × (1/1000) = 0.4 + 0.03 + 0.007
Now with the possibility of expressing decimals in expanded form, we can write any number in expanded form. A fraction, a percentage value can be converted into a decimal and the same can be written in the expanded form. A fraction of 1/7 in the decimal form would be 0.1428, 0.1428 in the expanded form would be 0.1428 = 1 × (1/10) + 4 × (1/10) 2 + 2(1/10) 3 + 8(1/10) 4 . And a percentage of 25% would be 0.25 = 2 × (1/10) + 5 × (1/10) 2
☛Related Topics
Given below is the list of topics that are closely connected to the expanded form. These topics will also give you a glimpse of how such concepts are covered in Cuemath.
Example 1: What is 5683 in the expanded form? Solution: The place value of each digit is identified with the help of the place value chart.
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 5 | 6 | 8 | 3 |
5683 = 5 × 1000 + 6 × 100 + 8 × 10 + 3 × 1 = 5000 + 600 + 80 + 3. Therefore the expanded form is 5000 + 600 + 80 + 3.
Example 2: Which expression is equivalent to 26,050? a) 20,000 + 6000 + 500 b) 20,000 + 600 + 50 c) 20,000 + 6000 + 50 Solution: Put each number from the list in the respective place value chart and fill in the chart.
| Ten Thousand | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 2 | 6 | 0 | 5 | 0 |
Now get the number in its expanded form. 26050 = 2 × 10000 + 6 ×1000 + 5 × 10 = 20,000+6000+ 50. Therefore we have 26,050 = 20,000 + 6000 + 50. Hence the option (c) - 20,000 + 6000+ 50 is the right answer.
Example 3: In the expanded form of the number 4569023 the digit 9 represents 9? Choose the correct answer from the following options. a) Thousands b) Hundreds c) Units d) Tens Solution: Put numbers from 3 to 9 in the respective place value chart and fill in the chart.
| Ten Thousand | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 6 | 9 | 0 | 2 | 3 |
Now get the last four numbers in expanded form. 9023 = 9 ×1000 + 0 × 100 + 2 × 10 + 3. Therefore, the digit 9 represents 9000 and the answer is a)Thousand.
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