CONVERTING STANDARD FORM TO SCIENTIFIC NOTATION

To learn how to convert a number from standard form into scientific notation, 

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Example 1 :

Write the following number in scientific notation.

205852

Solution :

Here, we don't find decimal point in 205852. So we have to assume that there is decimal point at the end . 

Then,

205852 ---------> 205852.

Here, non zero digit comes first and decimal point comes next. 

We have to move the decimal point to the left. 

No. of digits between the 1^st non zero digit and the decimal point is 5.

So, the decimal point has to be moved 5 digits to the left and exponent of 10 should be 5 (positive integer). 

Therefore, the scientific notation of 205852 is

2.05852 x 10⁵

Example 2 :

Write the following number in scientific notation.

3449098.96

Solution :

3449098.96

Here, non zero digit comes first and decimal point comes next. 

We have to move the decimal point to the left. 

No. of digits between the 1^st non zero digit and the decimal point is 6.

So, the decimal point has to be moved 6 digits to the left and exponent of 10 should be 6 (positive integer)

Therefore, the scientific notation of 3449098.96 is

3.44909896 x 10⁶

Example 3 :

Write the following number in scientific notation.

0.00008035

Solution : 

Here, decimal point comes first and non zero digit comes next. 

We have to move the decimal point to the right. 

No. of digits from the 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)

Therefore, the scientific notation of 0.00008035 is

8.035 x 10^-5

Example 4 :

Write the following number in scientific notation.

523600

Solution : 

Here, we don't find decimal point in 205852. So we have to assume that there is decimal point at the end . 

Then,

523600 ---------> 523600.

Here, non zero digit comes first and decimal point comes next. 

We have to move the decimal point to the left. 

No. of digits between the 1^st non zero digit and the decimal point is 5.

So, the decimal point has to be moved 5 digits to the left and exponent of 10 should be 5 (positive integer). 

Therefore, the scientific notation of 523600 is

5.236 x 10⁵

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