What Does Expanded Notation Mean

Definition of the Expanded Grade

In the expanded form. We suspension up a number according to its place value and aggrandize it to show the value of each digit. For instance, the expanded class of 943 is given.

9 blocks of hundreds four blocks of tens 3 blocks of ones

nine hundreds 4 tens iii ones expanded Form: 900 + xl + 3

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 nosotros motion from left to right. The digits on the left have a lower identify 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 sympathise the notations used in the place value using an example.

For the number 254, the identify value chart is:

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

Examples

Let'due south look at the number 875294831 as an example. This figure is tough to grasp. In this case, an expanded form assists u.s. 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 Discover an Expanded Form?

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

Get the number in its almost basic form.
Using the place value chart, decide its identify values.
Multiply the number by the number's place value.
Brandish information technology as a digit place value.
All digits should be represented equally the product of the digit and its identify value.

Expanded Form with Decimals

The expanded course of a number with a decimal or a fraction is written with a base ten-multiple denominator, represented by the ability of x.

For example, the number three.482 in expanded grade is written equally:

3.482 = three + 0.4 + 0.08 + 0.002

How to Write in an Expanded Form?

Suppose we want to expand 1.234. First, we accept one place i.e. one.

Next we have the first decimal place, the tenths.

We take two and multiply it by fraction $\frac{ane}{10}$.

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

And then, we accept the hundredth place. We move to a higher multiple of 10 for the denominator. In other words, we add together another 0.
1+(two $\times \frac{ane}{10}$) + (3 $\times \frac{1}{100}$)

Finally, we have the thousandth place. Add another 0 in the denominator.

1+(ii $\times \frac{1}{10}$) + (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:

Write 589 in its expanded class.

The expanded form of 589 would exist 500 + fourscore + 9.

Write 9677 in its expanded form.

The expanded form of 9677 would exist 9000 + 600 + lxx + vii.

Write 23.782 in its expanded form.

The expanded form of 23 would be 20 + iii + 0.vii + 0.08 + 0.002

Practice Bug

Expanded Form

Nourish this Quiz & Examination your knowledge.

$g + 80$

$chiliad + 100 + lxxx$

$1000 + 0 + 8$

$1000 + 0 + eighty + 0$

Right reply is: $1000 + 0 + 80 + 0$
The expanded course for $1080 = 1000 + 0 + 80 + 0$

$seven + 7$

$77 + 77$

$lxx + 7$

$seventy + 70$

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

$500 + 67 + 0.25$

$500 + 60 + seven + 0.2 + 0.05$

$560 + vii + 0.25$

$500 + 70 + 6 + 0.2 + 0.05$

Correct answer is: $500 + 60 + 7 + 0.ii + 0.05$
The expanded form for $567 = 500 + sixty + 7 + 0.two + 0.05$

Conclusion

Expanded form is naught only a technique to rewrite a number by including the values of the digits. Given above was everything you needed to know nigh expanded form. Students can learn about expanded form by solving more and more than problems. Luckily, SplashLearn is a platform created for students to make their bookish journeying worthwhile, piece of cake, and fun. Head over to SplashLearn to know more than.

Frequently Asked Questions

What is the significance of expanded course?

Expanded class is of import in maths considering it allows u.s. to await at a number and place the value of each digit.

What does writing in expanded form imply?

When we aggrandize a number to illustrate each digit's value, nosotros write information technology in expanded form.. With extended grade, nosotros 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 exist when it is expanded.

Are expanded grade and expanded notation the same?

No, expanded annotation is recognized equally 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 Instance of expanded note of 234 is 2 $\times$ 100 + 3 $\times$ 10 + 4 $\times$ 1