Use of Exponents to Express Small Numbers in Standard Form

The standard form of a number

When switching from a number to a normal notation (standard form) or vice versa, move the period to the right or left in the number and multiply it by 10 the appropriate degree.

If the number is less than 1, then writes it in the normal form 10 with a negative exponent.

If the given number is less than one, to convert that number to standard form, transfer the decimal to the right side of the number.

Consider a number 17845600; we can rewrite this number in standard form.

That is 17845600=1.78456×107.

Small number to standard form

Step 1: Observe whether the number is between 1 and 10 or it is less than 1.

Step 2: If the number is between 1 and 10, then write it as the product of the number itself and 100.

Step 3: If the number is between 0 and 1, then move the decimal point to the right side so that there is just one digit on the left side of the decimal point.

Write the given number as the product of the number obtained and 10-n, here n denotes the number of places the decimal point has been moved to the right side.

Standard form to usual form

 1. Expand the given 10n and multiply it by the given number.

 2. Then the result will be in the usual form.

Write the following numbers in usual form.

i) 1.0867×104

The given number is 1.0867×104.

Expand the 104 and multiply it by the given number.


Therefore, the usual form of 1.0867×104  is 10867.

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