Definition of the Expanded Form
In the expanded form. We break up a number according to its place value and expand it to show the value of each digit. For example, the expanded form of 943 is given.
9 blocks of hundreds 4 blocks of tens 3 blocks of ones
9 hundreds 4 tens 3 ones expanded Form: 900 + 40 + 3
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Place Value
Each number has a place value. It determines the value of that digit according to its position in the number. The value of a digit in a number increases as we move from left to right. The digits on the left have a lower place value than the digits on the right.
The value for each number is computed using the position of the number. Starting from right to left, we can understand the notations used in the place value using an example.
For the number 254, the place value chart is:
Thus, the expanded form of the number 254 is 200 + 50 + 4.
Examples
Let’s look at the number 875294831 as an example. This figure is tough to grasp. In this case, an expanded form assists us in understanding each of the numbers based on their place value.
875294831 can be written as 800000000 + 70000000 + 5000000 + 200000 + 90000 + 4000 + 800 + 30 + 1
The number has been expanded to reflect the value of each of its digits.
How to Find an Expanded Form?
Here are the steps to write a number in expanded form.
- Get the number in its most basic form.
- Using the place value chart, determine its place values.
- Multiply the number by the number’s place value.
- Display it as a digit place value.
- All digits should be represented as the product of the digit and its place value.
Expanded Form with Decimals
The expanded form of a number with a decimal or a fraction is written with a base 10-multiple denominator, represented by the power of 10.
For example, the number 3.482 in expanded form is written as:
3.482 = 3 + 0.4 + 0.08 + 0.002
How to Write in an Expanded Form?
Suppose we want to expand 1.234. First, we have one place i.e. 1.
Next we have the first decimal place, the tenths.
We take 2 and multiply it by fraction $\frac{1}{10}$.
1+(2 $\times \frac{1}{10}$)
Then, we have the hundredth place. We move to a higher multiple of 10 for the denominator. In other words, we add another 0.
1+(2 $\times \frac{1}{10}$) + (3 $\times \frac{1}{100}$)
Finally, we have the thousandth place. Add another 0 in the denominator.
1+(2 $\times \frac{1}{10}$) + (3 $\times \frac{1}{100}$) + (4 $\times \frac{1}{1000}$)
Hence, the expanded form of 1.234 is 1+0.2+0.03+0.004.
Solved Examples On Expanded Form
- Write 589 in its expanded form.
The expanded form of 589 would be 500 + 80 + 9.
- Write 9677 in its expanded form.
The expanded form of 9677 would be 9000 + 600 + 70 + 7.
- Write 23.782 in its expanded form.
The expanded form of 23 would be 20 + 3 + 0.7 + 0.08 + 0.002
Practice Problems On Expanded Form
Expanded Form
Write 1080 in its expanded form.
The expanded form for $1080 = 1000 + 0 + 80 + 0$
Write 77 in its expanded form.
The expanded form for $77 = 70 + 7$
Write 567.25 in its expanded form.
The expanded form for $567 = 500 + 60 + 7 + 0.2 + 0.05$
Conclusion
Expanded form is nothing but a technique to rewrite a number by including the values of the digits. Given above was everything you needed to know about expanded form. Students can learn about expanded form by solving more and more problems. Luckily, SplashLearn is a platform created for students to make their academic journey worthwhile, easy, and fun. Head over to SplashLearn to know more.
Frequently Asked Questions On Expanded Form
What is the significance of expanded form?
Expanded form is important in math because it allows us to look at a number and identify the value of each digit.
What does writing in expanded form imply?
When we expand a number to illustrate each digit’s value, we write it in expanded form.. With extended form, we represent the numerical value of each digit in the number we’re writing. Except for zeroes, the larger the number is, the longer its expanded form will be when it is expanded.
Are expanded form and expanded notation the same?
No, expanded notation is recognized as a number that represents the sum of every digit in a particular number further multiplied by its respective place value.
Example of expanded form of 234 = 200 + 30 + 4 Example of expanded notation of 234 is 2 $\times$ 100 + 3 $\times$ 10 + 4 $\times$ 1