Expanded Form of a Number: Any number in Mathematics can be written in expanded form. The expanded form helps us understand a given number in Mathematics better. Expanded form is important in Maths because it allows us to look at a number and identify the value of each digit. Let us take an example of the number \({\rm{1078295832}}{\rm{.}}\) 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 \(534\) and try to find its expanded form. \(534\) is written in expanded form as \({\rm{500 + 30 + 4}}.\) It means there are five hundreds, three tens, and \(4\) ones in this number. We can easily understand the meaning of each digit of a number through its expanded form.

What is Meant by Expanded Form?

Trying to learn a number with a higher number of digits is complicated without knowing how to express it in expanded form. The expanded form helps us to see the building blocks of higher numbers. We can write each of the digits in the multiple forms of \({\rm{1,}}\,{\rm{10,}}\,{\rm{100,}}\,{\rm{1000}}.\) Now, with this understanding, let us move ahead to know more about the expanded form.

How to Write Numbers in Expanded Form?

Showing the number as a sum of each digit multiplied by its place value is the expanded form of a number. We can write the value of each digit in Mathematics in expanded form.

The expansion of a \(2\)-digit number \(78\) is
\(78 = 70 + 8 = 7 \times 10 + 8\)

Similarly, the expansion of a \(3\)-digit number \(278\) is
\(278 = 200 + 70 + 8 = 2 \times 100 + 7 \times 10 + 8\)
Here, \(8\) is at ones place, \(7\) is at tens place and \(2\) at hundreds place.
Let us extend this idea to \(4\)-digit numbers.

For example, the expansion of \(5278\) is
\(5278 = 5000 + 200 + 70 + 8 = 5 \times 1000 + 2 \times 100 + 7 \times 10 + 8\)
Here, \(8\) is at ones place, \(7\) is at tens place, \(2\) is at hundreds place, and \(5\) is at thousands place.
As the number \(10000\) known to us, we may extend the idea further to write 5-digit numbers like
\(45278 = 4 \times 10000 + 5 \times 1000 + 2 \times 100 + 7 \times 10 + 8\)

We say that here \(8\) is at ones place, \(7\) at tens place, \(2\) at hundreds place, \(5\) at thousands place and \(4\) at ten thousands place. The number is read as forty-five thousand, two hundred seventy-eight.

Expanded Form Uses 

The expanded form helps to split and present the higher digit number in its units, tens, hundreds, thousands, etc. Thus, an expanded form helps to understand better and read the higher digit numbers properly. For example, a number of the form \(1003000\) is sometimes difficult to understand directly and can be represented in expanded form as

\(1003000 = {\rm{10,00000}} + 3000\)
Some more examples of the expanded form are provided in the following table.

Expanded Form of a Number

The expansion of a number is the separation of numbers based on place values. This is the intermediate step that helps us understand how we can read the number. The expanded form allows us to know the place value of each digit within a number. Further, we can write numbers in the expanded form in three different ways.

The number \(6531\) can be written in one way of expanded form as
\(6531 = 6000 + 500 + 30 + 1\)
In the second way as
\(6531 = 6 \times 1000 + 5 \times 100 + 3 \times 10 + 1 \times 1\)

And in the third way as
\(6531 = 6 \times {\rm{thousands}} + 5 \times {\rm{hundreds}} + 3 \times {\rm{tens}} + 1 \times {\rm{ones}}\)
Here are the steps, which you can follow to find the expanded form:
1. Get the number in its standard form.
2. Determine its place values using the place value chart.
3. Multiply the number by its place value.
4. Show it as digit \( \times \) times place value.
5. Represent all the digits as the product of the digit and its place value.

We can decompose any number for ease of reading. This process of decomposing the number is called the expanded form of the number. After decomposing in the expanded form, we understand the number in its standard form.

Expanded Form of Decimal Numbers

Decimal numbers can be expressed in expanded form using the place-value chart.
The place value system is used to define the position of a digit in a number which helps to determine its value. When we write specific numbers, the position of each digit is important.

We can find the power of \(10\) associated with each digit in a number using the following place value chart:

The digits present to the left of the decimal point are multiplied with the positive powers of \(10\)\ in increasing order from right to left. The digits present to the right of the decimal point are multiplied with the negative powers of \(10\) in increasing order from left to right.

Let us consider the number \(12.45.\) Let us expand each digit using the place-value chart as
\(1 \times 10 + 2 + 4 \times \frac{1}{{10}} + 5 \times \frac{1}{{100}} = 10 + 2 + 0.4 + 0.05 = 12.45\)

Now, we can write any number in the expanded form, whether it is a decimal number or a whole number. In the decimal expansion of fractions or percentages, we can convert a fraction or a percentage value into a decimal, and we can write the same in the expanded form.

Expanded Form Calculator

The expanded form calculator’s rules are simple to understand. All you have to do is follow these three simple steps:

1. In the “Number” field, type the number you want in expanded notation.
2. Select the appropriate term in “form” to get the answer you want: numbers, factors, or exponents.
3. Get the result.

Solved Examples – Expanded Form of a Number

Q.1. A number has \(5\) thousands, \(5\) hundreds, \(3\) tens and \(4\) ones. What is the number?
Ans: The place value of the following numbers are:
\(5\,{\rm{thousands}} = 5,000\)
\(6\,{\rm{thousands}} = 6000\)
\(3\,{\rm{ tens }} = 30\)
\(4\,{\rm{ones}} = 4\)
Adding these numbers together, we get: \({\rm{5,000 + 600 + 30 + 4 = 5634}}.\) Therefore, the number is \(5634.\)

Q.2. Fill in the blank with the missing place value in the given addition of the numbers.
\({\rm{800 + \_\_\_\_ + 1 = 891}}{\rm{.}}\)
Ans: The number 891 can be written in the expanded form as
\(891 = 8 \times 100 + 9 \times 10 + 1\)
\({\rm{891 = 800 + 90 + 1}}\)
The missing number is \(9,\) and the place value of \(9,\) is \(9 \times 10 = 90.\) Therefore, the missing place value is \(90.\)

Q.3. What is \(5683\) in the expanded form?
Ans: We can identify the place value of each digit with the help of the place value chart.

Thousands	Hundreds	Tens	Ones
\(5\)	\(6\)	\(8\)	\(3\)

\(5683 = 5 \times 1000 + 6 \times 100 + 8 \times 10 + 3 \times 1 = 5000 + 600 + 80 + 3.\)
Therefore the expanded form is \({\rm{5000 + 600 + 80 + 3}}{\rm{.}}\)

Q. 4. Write the expanded form of the decimal number \(3645.82.\)
Ans: The decimal expansion of the number can be done by following two steps.
The digits present to the left of the decimal point are multiplied with the positive powers of \(10\) in increasing order from right to left.

The digits present to the right of the decimal point are multiplied with the negative powers of \(10\) in increasing order from left to right.
Hence, the expansion of the number is given below:
\(\left\{ {(3 \times 1000) + (6 \times 100) + (4 \times 10) + (5 \times 1) + \left( {8 \times \frac{1}{{10}}} \right) + \left( {2 \times \frac{1}{{100}}} \right)} \right\}\)

Q.5. Write the decimal expansion of the number \(35.82.\)
Ans: The decimal expansion of the number can be done by following two steps.
The digits present to the left of the decimal point are multiplied with the positive powers of \(10\) in increasing order from right to left.

The digits present to the right of the decimal point are multiplied with the negative powers of \(10\) in increasing order from left to right.
Hence, the expansion of the number is given below:
\(\left\{ {(3 \times 10) + (5 \times 1) + \left( {8 \times \frac{1}{{10}}} \right) + \left( {2 \times \frac{1}{{100}}} \right)} \right\}.\)

Q.6. Write the expanded form of the numbers \(10000,\,13\) and \(90.\)
Ans: The expanded form of \(10000 = 1 \times 10000\)
The expanded form of \(13 = 1 \times 10 + 3\)
The expanded form of \(90 = 9 \times 10\)

Summary

In this article, we learned the meaning and definition of the expanded form of a number, and how to write the number in expanded form using the place value chart like tens, hundred, thousand, etc. We have learnt to write the numbers in the expanded form. Also, we have discussed the expanded form of decimal numbers using the decimal place value chart with the help of illustrations.

Frequently Asked Questions (FAQ) – Expanded Form of a Number

Q.1. What are examples of the expanded form of a number?
Ans: The examples of the expanded form of a number are
\(324 = 3 \times 100 + 2 \times 10 + 4\)
\(4456 = 4 \times 1000 + 4 \times 100 + 5 \times 10 + 6\)
\(1023 = 1 \times 1000 + 2 \times 10 + 3\)

Q.2. Why is expanded form important?
Ans: Expanded form is important in Maths because it allows us to look at a number and identify the value of each digit.

Q.3. What are the uses of the expanded form of a number?
Ans: The expanded form of a number is used to add large numbers.

Q.4. Write \(300\) in expanded form.
Ans: The expanded form of \(300\) is \(3 \times 100.\)

Q.5. What is the place value?
Ans: Place value is the value of a digit according to its position in the number, such as ones, tens, hundreds, and so on.
For example, \(4\) in \(3458\) represents \(4\) hundreds.

We hope you find this detailed article on the expanded form of a number proves helpful to you. If you have any doubts or queries regarding this topic, feel to ask us in the comment section and will help you at the earliest.