SCIENTIFIC NOTATION WITH POSITIVE POWERS OF 10 WORKSHEET

Problem 1 :

Write the given number in scientific notation. 

5400000

Problem 2 :

Write the given number in scientific notation. 

35614.23

Problem 3 :

Write the given number in scientific notation. 

203005.1

Problem 4 :

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. 

Detailed Answer Key

Problem 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)

Problem 2 :

Write the given number in scientific notation. 

35614.23

Solution :

In the given number 35614.23, number of digits between the first non zero digit and the 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)

35614.23  =  3.561423 x 10⁴

Hence, the scientific notation of 35614.23 is

3.561423 x 10⁴

Problem 3 :

Write the given number in scientific notation. 

203005.1

Solution :

In the given number 203005.1, number of digits between the first 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)

203005.1  =  2.030051 x 10⁵

Hence, the scientific notation of 203005.1 is

203005.1  =  2.030051 x 10⁵

Problem 4 :

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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