What Is An Expanded Notation

Definition of the Expanded Course

In the expanded form. We break up a number according to its place value and expand information technology 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 iii ones expanded Class: 900 + twoscore + iii

Place Value

Each number has a identify 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 nosotros move from left to right. The digits on the left take a lower place value than the digits on the correct.

The value for each number is computed using the position of the number. Starting from right to left, we tin understand the notations used in the place value using an instance.

For the number 254, the place value chart is:

Thus, the expanded form of the number 254 is 200 + 50 + 4.

Examples

Allow's look at the number 875294831 as an example. This figure is tough to grasp. In this example, an expanded grade assists us in agreement 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 Discover an Expanded Grade?

Here are the steps to write a number in expanded form.

Get the number in its about bones form.
Using the place value chart, decide its place values.
Multiply the number by the number'due south place value.
Brandish it every bit a digit place value.
All digits should exist represented every bit the production 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 of operations 10-multiple denominator, represented by the ability 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 one.234. First, we have one place i.e. i.

Next we take the offset decimal place, the tenths.

Nosotros accept ii and multiply it by fraction $\frac{one}{x}$.

i+(2 $\times \frac{1}{10}$)

And so, we take the hundredth identify. We move to a higher multiple of 10 for the denominator. In other words, we add another 0.
1+(ii $\times \frac{ane}{10}$) + (3 $\times \frac{1}{100}$)

Finally, nosotros take the thousandth place. Add together another 0 in the denominator.

i+(2 $\times \frac{ane}{10}$) + (three $\times \frac{ane}{100}$) + (four $\times \frac{1}{1000}$)

Hence, the expanded class of one.234 is 1+0.two+0.03+0.004.

Solved Examples:

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 + vii.

Write 23.782 in its expanded form.

The expanded grade of 23 would be 20 + 3 + 0.seven + 0.08 + 0.002

Practice Problems

Expanded Form

Attend this Quiz & Test your knowledge.

$1000 + 80$

$1000 + 100 + lxxx$

$yard + 0 + eight$

$1000 + 0 + fourscore + 0$

Correct answer is: $1000 + 0 + 80 + 0$
The expanded form for $1080 = 1000 + 0 + 80 + 0$

$7 + 7$

$77 + 77$

$70 + 7$

$70 + 70$

Right answer is: $seventy + 7$
The expanded form for $77 = 70 + seven$

$500 + 67 + 0.25$

$500 + sixty + 7 + 0.2 + 0.05$

$560 + 7 + 0.25$

$500 + lxx + 6 + 0.2 + 0.05$

Correct answer is: $500 + 60 + seven + 0.2 + 0.05$
The expanded course for $567 = 500 + 60 + 7 + 0.2 + 0.05$

Conclusion

Expanded class is nothing but a technique to rewrite a number by including the values of the digits. Given in a higher place was everything you needed to know nigh expanded form. Students can larn nearly 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

What is the significance of expanded class?

Expanded form is of import in maths because it allows us to expect at a number and place the value of each digit.

What does writing in expanded form imply?

When nosotros expand a number to illustrate each digit'due south value, we write information technology 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 class will be when it is expanded.

Are expanded course 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.

Case of expanded form of 234 = 200 + 30 + four Instance of expanded annotation of 234 is two $\times$ 100 + 3 $\times$ x + four $\times$ 1