In Mathematics, the value of each digit in the number can be written in the expanded form. The numbers that are represented as the sum of each digit multiplied by its place value is called the expanded form of the numbers. In this article, we are going to discuss the expanded form of the number, expanded form of decimal numbers, expanded factor form, expanded exponential form with many solved examples in detail.
Table of Contents:
- Expanded Form of Numbers
- How to Write the Numbers in Expanded Form?
- Expanded Form of Decimal Numbers
- Expanded Factor Form
- Expanded Exponential Form
- Practice Problems
- FAQs
Expanded Form of Numbers
The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. For example, the expanded form of the number 1572 is 1000+500+70+2.
Some of the examples of the expanded form of numbers are provided in the tabular form:
Number |
Ten thousand | Thousands | Hundreds | Tens | Ones |
723 |
7 | 2 | 3 | ||
1243 |
1 |
2 | 4 | 3 | |
5679 |
5 |
6 | 7 | 9 | |
23456 |
2 |
3 | 4 | 5 | 6 |
Let us take the number 723. In number 723, there are 7 hundreds, 2 tens and 3 ones.
More Examples on Expanded Form:
- The expanded form of 90 is 90+0. In the number 90, there are 9 tens and zero ones.
- 300 in the expanded form is 300+0+0, as there are zero tens and zero ones.
- The expanded form of 10,000 is 10000+0+0+0+0. In the number 10,000, there are zero thousand, zero hundred, zero tens and zero ones.
How to Write Numbers in Expanded Form?
Go through the below steps to write the numbers in expanded form:
Step 1: Get the standard form of the number.
Step 2: Identify the place value of the given number using the place value chart.
Step 3: Multiply the given digit by its place value and represent the number in the form of (digit × place value).
Step 4: Finally, represent all the numbers as the sum of (digit × place value) form, which is the expanded form of the number.
Example:
What is 35713 in expanded form?
Solution:
Step 1: The standard form of the number is 35713.
Step 2: The place value of the given number is:
3 – Ten thousand
5 – Thousands
7 – Hundreds
1 – Tens
3 – Ones
Step 3: Multiply the given number by its place value.
(i.e.,) 3×10, 000, 5×1000, 7×100, 1×10, 3×1
Step 4: Expanded form is 30,000+ 5000+700+10+3
Finally, the expanded form of the number 35713 is 30,000+ 5000+700+10+3.
Expanded Form of Decimal Numbers
The decimal numbers can also be written in the expanded form. While writing the decimals in the expanded form, we need to multiply each decimal digit with the increasing exponent values of 1/10. Using the place value chart, the digits after the decimal points are represented as tenth (1/10), hundredth (1/100), thousandth (1/1000) and so on.
Now, let us consider the example 83.34.
First, write the expanded form for the number before the decimal point. (i.e.) 83
The expanded form of 83 is 80+3.
Now, the expanded form 34 is written as 3(1/10) + 4(1/100) [As 3 represents the tenth position and 4 represents the hundredth position]
Thus, the expanded form of 83.34 is written as 80+3+(3/10)+(4/100)
The above-expanded form can also be represented as 80+3+0.3+0.04.
Expanded Factor Form
In expanded factor form, the standard form of the number is written in its expanded factor form. If the number is written as the sum of the product of digit and its place value, then it is called expanded factor form.
Expanded Factor Form = Sum of (Digit × Place value)
Also, read: |
Expanded Exponential Form
In expanded exponential form, the place value of the digits is represented in terms of the powers of 10. It means that one’s place is represented by 10^{0}, tens place is represented by 10^{1}, hundreds place is represented by 10^{2}, and so on.
For example, the expanded exponential form of 2325 is represented by:
2 – Thousands (2 ×10^{3})
3 – Hundreds (3 × 10^{2})
2 – Tens (2 × 10^{1})
5 – Ones (5 × 10^{0})
Thus, the expanded exponential form of 2325 is (2 ×10^{3})+(3 × 10^{2})+ (2 × 10^{1})+ (5 × 10^{0})
Practice Problems
Solve the following problems:
- Expand the number 98234.
- Expand the decimal number 14.269.
- Expand the number 4674 in the exponential form.
- Expand the decimal number 3.726 in the exponential form.
- Convert the number 2.7690 into the expanded form.
Frequently Asked Questions on Expanded Form
What is meant by expanded form?
The expanded form of the number is the splitting of numbers based on the place value, such as ones, tens, hundreds, thousands, ten thousand, and so on. The number that is represented by the sum of each digit multiplied by its place value is called the expanded form of the number.
Mention the difference between the standard form and the expanded form of the numbers.
The standard form of the number is the combination of digits that together forms a number. Whereas the expanded form of the number is the separation of individual digits with their place value.
What are the expanded form and expanded notation of the number 4987?
The expanded form of 4987 is 4000+900+80+7.
The expanded notation of 4987 is (4×1000)+(9×100)+(8×10)+(7×1).
What is the expanded form of 5367?
The expanded form of the number 5367 is 5000+300+60+7.
What is the expanded form of 29.72?
The expanded form of the decimal number 29.72 is 20 + 9 + 0.7 + 0.02.