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Home > News & Articles > Expanded Form: Definitions, Examples, Factor Form, Decimal Form, Exponential Form, Calculator, and Benefits
Updated on 29th August, 2023 , 5 min read
The value of each digit of a number can be written in expanded form in mathematics. The expanded version of the numbers are the numbers that are represented as the sum of each digit multiplied by its place value. We will go through the expanded form of a number, the expanded form of decimal numbers, the expanded factor form, and the expanded exponential form in-depth, with many sample questions.
The process of breaking down or splitting integers into their right place value is known as expanded form. It is frequently used to perform huge sums in the absence of a calculator. It can also help us comprehend the distinction between thousands, hundreds, tenths, single units, and decimal places.
For example: Consider the number 987654321.. This statistic is difficult to fathom. In this situation, an enlarged form helps us grasp each number depending on its place value. The number 987654321 may also be written as-
The number has been enlarged to show the value of each digit.
The extended form of the numbers aids in determining the position of each digit in the provided number. It signifies that number growth is dependent on place value. The enlarged form divides the number into units, tens, hundreds, and thousands. The extended version of the number 1572, for example, is 1000+500+70+2.
Some instances of extended forms of numerals are shown in the table below-
Consider the number 123. There are 1 hundreds, 2 tens, and 3 ones in the number 123.
The following are some more examples of Expanded Forms-
The conventional form of the number is written in its expanded factor form. When a number is represented as the product of a digit and its place value, it is written in expanded factor form.
A sum of (Digit Place value + Expanded Factor Form).
The following are some of the numbers in expanded form-
Step 1: Determine the number's standard form.
Step 2: Using the place value table, determine the place value of the provided integer.
Step 3: Multiply the provided digit by its place value and write the result as (digit place value).
Step 4: Finally, express all of the numbers as the sum of (digit place value) form, which is the number's expanded form.
Example: What is the extended form of 34287?
Solution-
Step 1: 34287 is the usual form of the number.
Step 2: The supplied number's place value is-
3 - Ten Thousand
4 - Thousands
2 - Hundreds
8 - Tens
7 - Ones
Step 3: Take the supplied integer and multiply it by its place value.
(i.e.,) 3×10, 000, 4×1000, 2×100, 8×10, 7×1
Step 4: 30,000 + 4000 + 200 + 80 + 7 is the expanded form.
Finally, 34287 has the enlarged form 30,000 + 4000 + 200 + 80 + 7.
The procedures for writing any whole number in expanded form are as follows-
The extended form of decimal numerals can also be written. When expressing decimals in expanded form, we must multiply each decimal digit by an increasing exponent of 1/10. The digits following the decimal points are represented on the place value chart as tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on.
Consider the following example: 59.30.
The place value of the digits is expressed in expanded exponential form by powers of 10. It implies that the number one is represented by 10⁰, the number ten is represented by 10¹, the number hundred is represented by 10², and so on. The extended exponential form of 8973, for example, is represented by-
8 – Thousands (8 ×10³)
9 – Hundreds (9 × 10²)
7 – Tens (7 × 10¹)
3 – Ones (3 × 10⁰)
As a result, the extended exponential form of 8973 is (8 ×10³) + (9 × 10²) + (7 × 10¹) + (3 × 10⁰).
The rules of the extended form calculator are straightforward. All you have to do is take the following three simple steps-
The following are some of the benefits of expanded form-
Solve the following questions-
Practice Question 1: In exponential form, expand the decimal value to 1.347.
Practice Question 2: In exponential form, expand the number 8709.
Practice Question 3: Expand the number 58945.
Practice Question 4: Convert the extended form of the number 5.7987.
Practice Question 5: Expand the decimal number 38.095.
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readAns. No, expanded notation is recognized as a number that reflects the sum of each digit in a specific number multiplied by its place value.
Ans. The standard form of a number is the set of digits that make up a number. The expanded version of the number, on the other hand, is the separation of individual digits with their place value.
Ans. To better grasp the supplied number, we require an extended form. The extended version explains the value of each digit based on its place value. The extended form is highly important in the early stages of learning numbers since it allows you to understand more about each of the digits inside the number.
Ans. The extended form of decimal numerals can also be written. When expressing decimals in expanded form, we must multiply each decimal digit by an increasing exponent of 1/10. The digits following the decimal points are represented on the place value chart as tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on.
Ans. The extended form of a number is the division of a number into place values, such as ones, tens, hundreds, thousands, ten thousand, and so on. The number represented by the sum of each digit multiplied by its place value is known as its expanded form.
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