SCIENTIFIC NOTATION WITH NEGATIVE POWERS OF 10

This is the method of expressing a very small number as a product of a number greater than or equal to 1 and less than 10, and a negative power of 10.

A number whose value is between 0 and 1 is written in scientific notation when it is expressed in the form 

a x 10ⁿ 

where 1 ≤ a < 10 and n is a negative integer. 

To convert a number (whose value is between 0 and 1) into scientific notation, we have to move the decimal point to the right and multiply by 10 with negative power. 

To move the decimal point to the right, we have to count number of digits as explained in the example given below. 

According to the example given above, we have to move the decimal point 5 digits to the left and exponent of 10 should be -5 (negative integer)

When we do so, we get the scientific notation of the given number. 

Therefore,

0.000023  =  2.3 x 10^-5

Solved Examples

Example 1 :

Write the given number in scientific notation. 

0.00006

Solution :

In the given number 0.00006, number of digits from decimal point up to the first non zero digit is 5.

So, the decimal point has to be moved 5 digits to the right and exponent of 10 should be -5 (negative integer)

0.00006  =  6.0 x 10^-5

Hence, the scientific notation of 0.00006 is

6.0 x 10^-5

Example 2 :

Write the given number in scientific notation. 

0.00000092

Solution :

In the given number 0.00000092, number of digits from decimal point up to the first non zero digit is 7.

So, the decimal point has to be moved 7 digits to the right and exponent of 10 should be -7 (negative integer)

0.00000092  =  9.2 x 10^-7

Hence, the scientific notation of 0.00000092 is

9.2 x 10^-7

Example 3 :

Write the given number in scientific notation. 

0.002006

Solution :

In the given number 0.002006, number of digits from decimal point up to the first non zero digit is 3.

So, the decimal point has to be moved 3 digits to the right and exponent of 10 should be -3 (negative integer)

0.002006  =  2.006 x 10^-3

Hence, the scientific notation of 0.002006 is

2.006 x 10^-3

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