USING SCIENTIFIC NOTATION

Scientific notation is a method of expressing very large and very small numbers as a product of a number greater than or equal to 1 and less than 10, and a power of 10.

Scientific Notation Rules

A number is written is scientific notation when it is expressed in the form 

a x 10ⁿ 

where 1 ≤ a < 10 and n may be a positive or negative integer.

To convert the given number into scientific notation, first we have to identify where the decimal point and non zero digit come. 

There are two cases in it. 

Case 1 : 

To move the decimal point to the left, 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 3 digits to the left and exponent of 10 should be 3 (positive integer)

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

Therefore,

2301.8  =  2.3018 x 10³

Case 2 : 

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 right 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

Important Note: 

If we don't find decimal point at anywhere of the given number, we have to assume that there is decimal point at the end of the number.

For example, 

2300000 -------------> 2300000.

Here, the non zero digit comes first and decimal point comes next. So we have to apply case 1 to convert this number into scientific notation.  

Solved Problem

The weights of various sea creatures are shown in the table. Write the weight of the Blue whale, Gray whale and Whale shark in scientific notation.

Weight of Blue whale in scientific notation : 

In the given weight of Blue whale (250,000 lb), we don't find decimal point. So we have to assume that there is decimal point at the end . 

Then,

250,000 -----> 250,000.

Number of digits between the first non zero digit and 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)

250,000  =  2.50000 x 10⁵

250,000  =  2.5 x 10⁵

(Here, zeros after the decimal point are not taken. Because, they are not valid zeros)

Hence, the weight of Blue whale in scientific notation is

2.5 x 10⁵ lb

Weight of Gray whale in scientific notation : 

In the given weight of Gray whale (68,000 lb), we don't find decimal point. So we have to assume that there is decimal point at the end . 

Then,

68,000 -----> 68,000.

Number of digits between the first non zero digit and decimal point is 4.

So, the decimal point has to be moved 4 digits to the left and exponent of 10 should be 4 (positive integer)

68,000  =  6.8000 x 10⁴

68,000  =  6.8 x 10⁴

(Here zeros after the decimal point are not taken. Because, they are not valid zeros)

Hence, the weight of Gray whale in scientific notation is 

6.8 x 10⁴ lb

Weight of Whale shark in scientific notation : 

In the given weight of Whale shark (41,200 lb), we don't find decimal point. So we have to assume that there is decimal point at the end . 

Then,

41,200 -----> 41,200.

Number of digits between the first non zero digit and decimal point is 4.

So, the decimal point has to be moved 3 digits to the left and exponent of 10 should be 4 (positive integer)

41,200  =  4.1200 x 10⁴

41,200  =  4.12 x 10⁴

(Here, zeros after the decimal point are not taken. Because, they are not valid zeros)

Hence, the weight of Gray whale in scientific notation is 

4.12 x 10⁴ lb

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