Thus, every large number can be expressed as k x 10ⁿ, where k is some natural number. However, for the sake of uniformity, we write the numbers in the form k x 10ⁿ, where k is a terminating decimal number greater than or equal to 1 and less than 10 and n is a natural number.

Such a form of a number is known as its standard form.

Standard Form

A number is said to be in the standard form, if it is expressed as the product of a number between 1 and 10 (including 1 but excluding 10) and a positive integer power of 10.

The standard form of a number is also known as Scientific Notation.

By using the following steps, we can write large numbers in the standard form or Scientific Notation:

Step I: Obtain the number and move the decimal point to the left till you get just one digit to the left of the decimal point.

Step II: Write the given number as the product of the number so obtained and 10ⁿ, where n is the number of places the decimal point has been moved to the left. If the given number is between 1 and 10, then write it as the product of the number itself and 10⁰.

Example 1:

Express the following number in standard form:
3, 90, 878

390878 = 390878.00

The decimal point is moved through five places to obtain a number in which there is just one digit to the left of the decimal point.

Therefore, 390878.00 = 3.90878 x 10⁵

Example 2:

Write the following number in the usual form:
7.54 x 10⁶

7.54 x 10⁶ = 7, 540, 000
       


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Reference Links:

•     http://en.wikipedia.org/wiki/Scientific_notation
•     http://en.wikipedia.org/wiki/Repeating_decimal
•     http://en.wikipedia.org/wiki/Large_numbers
•     http://en.wikipedia.org/wiki/Exponentiation