**Scientific notation with positive powers of 10 :**

Scientific notation with a positive power of 10 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 is written is scientific notation when it is expressed in the form

**a x 10 ^{n }**

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

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

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.

**Hence, 2301.8 = 2.3018 x 10³**

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.

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 1st non zero digit and decimal point = 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 = 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 blue 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.

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 1st non zero digit and decimal point = 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 = 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 blue whale (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.

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 1st non zero digit and decimal point = 4

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

41,200 = 4.1200 x 10⁴ = 4.12 x 10⁴

(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 4.12 x 10⁴ lb.

After having gone through the stuff given above, we hope that the students would have understood "Scientific notation with positive powers of 10"

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