Exponential Form

Exponential Form

By Hannah M

Exponential Form

​Expanded Form

• Positive whole numbers in expanded notation can be expressed using exponential notation and vice versa.

Example 1:

Write the expanded form of the numeral 5764

Solution:

5764 = 5000 + 700 + 60 + 4

= (5 x 1000) + (7 x 100) + (6 x 10) + (4 x 1)

Exponential form can also be called Exponential expression (or notation).

Exponential Form

​Expanded form

Example 2:

Write the expanded form of the numeral 603 875 805

Solution:

603 875 805 = 600 000 000 + 3 000 000 + 800 000 + 70 000 +

5 000 + 800 + 5

= 6 x 100 000 000) + (3 x 1 000 000 000) + (8 x 100 000) + 

7 x 10 000) + (5 x 1000) + (8 x 100) + (5 x 1) 

Expressions like 5^2 is called exponential expression

Exponential form

​EXPLANATION

In the given examples, the expanded form of the numeral is obtained by multiplying each digit of the given number by its place value and adding the products. The parenthesis means that the digits inside are considered as a numeral.

The numeral 655 492 can be written as:

65 492 = (6 x 10 000) + (5 x 1000) + (4 x 100) + (9 x 10) + (2 x 1) 

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Exponential Form

​Explanation

If we define,

10 x 10 = 102

10 x 10 x 10 = 103

10 x 10 x 10 x 10 = 104, and so on.

then 65 492 = (6 x 104) + (5 x 103) + (4 x 102) + (9 x 101) 

+ (2 x 100)

This is called the exponential notation of the number 65 492.

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Quiz!

Try to solve this questions.

Fill in the Blanks

Exponential form of $6^4$  :

$6^4$ = 1296

Explanation

This symbol (^) is called a carat. it is use in typing exponents in any device.

Thank you!

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