CONVERTING SCIENTIFIC NOTATION TO STANDARD FORM

To convert a number from scientific notation to standard notation, first we have to notice the exponent of 10 in scientific notation.

If the exponent of 10 is positive, we have to move the decimal point to the right. 

For example, if you have 10³, you have to move the decimal point 3 digits to the right. 

If the exponent of 10 is negative, we have to move the decimal point to the right. 

For example, if you have 10^-5, you have to move the decimal point 5 digits to the left. 

Solved Examples

Example 1 :

Write the following number in standard form.  

5.236 x 10⁵

Solution :

Here, the exponent of 10 is positive 5. So we have to move the decimal point five digits to the right.

In 5.236, we have only three digits after the decimal point.

So, we have to add two zeros to move the decimal point five digits to the right.   

Therefore, the standard form of 5.236 x 10⁵ is 

523600

Example 2 :

Write the following number in standard form.  

6.415 x 10^-6

Solution :

Here, the exponent of 10 is negative 6. So we have to move the decimal point six digits to the left.

In 6.415, we have only 1 digit before the decimal point.

So, we have to add five zeros to move the decimal point six digits to the left.   

Therefore, the standard form of 6.415 x 10^-6 is 

0.000006415

Example 3 :

Write the following number in standard form.  

1.72 x 10⁹

Solution :

Here, the exponent of 10 is positive 9. So we have to move the decimal point nine digits to the right.

In 1.72, we have only two digits after the decimal point.

So, we have to add seven zeros to move the decimal point nine digits to the right.   

Therefore, the standard form of 1.72 x 10⁹ is 

1720000000

Example 4 :

Write the following number in standard form.  

0.00023 x 10⁷

Solution :

Here, the exponent of 10 is positive 7. So we have to move the decimal point seven digits to the right.

In 0.00023, we have only five digits after the decimal point.

So, we have to add two zeros to move the decimal point seven digits to the right.   

Therefore, the standard form of 0.00023 x 10⁷ is 

2300

Example 5 :

Write the following number in standard form.  

0.036 x 10^-3

Solution :

Here, the exponent of 10 is negative 3. So we have to move the decimal point three digits to the left.

In 0.036, we don't have any non zero digit before the decimal point.

So, we have to add three zeros to move the decimal point three digits to the left.   

Therefore the standard form of 0.036 x 10^-3 is 

0.000036

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