SCIENTIFIC NOTATION WITH POSITIVE POWERS OF 10

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

A number whose value is greater than 10 is written in scientific notation when it is expressed in the form 

a x 10ⁿ 

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

To convert a number (whose value is greater than 10) into scientific notation, we have to move the decimal point to the left and multiply by 10 with positive power. 

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

Solved Examples

Example 1 :

Write the given number in scientific notation. 

5400000

Solution :

Here we don't find decimal point in 5400000. So we have to assume that there is decimal point at the end . 

Then, 5400000 ---------> 5400000.

Number of digits between the first 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)

5400000  =  5.400000 x 10⁶

5400000  =  5.4 x 10⁶

Hence, the scientific notation of 5400000 is

5.4 x 10⁶

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

Example 2 :

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.

Write the weight of each creature in scientific notation. 

Solution : 

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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