SCIENTIFIC NOTATION WORKSHEET

Problem 1 :

Write the given number in scientific notation. 

0.00006

Problem 2 :

Write the given number in scientific notation. 

5400000

Problem 3 : 

Write the given number in scientific notation. 

71 x 102

Problem 4 :

Write the given number in scientific notation. 

33 x 10-3

Problem 5 :

Write the given number in scientific notation. 

0.63 x 10-3

Problem 6 :

Write the given number in scientific notation. 

0.000216

Problem 7 :

Write the given number in scientific notation. 

0.0000009

Problem 8 :

Write the given number in scientific notation. 

804 x 102

Problem 9 :

Write the given number in scientific notation. 

4.8

Problem 10 :

Write the given number in scientific notation. 

0.99 x 10

Detailed Answer Key

Problem 1 :

Write the given number in scientific notation. 

0.00006

Solution :

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

We have to move the decimal point to the right. 

Number 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)

Hence, the scientific notation of 0.00006 is

6.0 x 10-5

Problem 2 :

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.

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

We have to move the decimal point to the left. 

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 3 : 

Write the given number in scientific notation. 

71 x 102

Solution :

Here, we don't find decimal point in 71x 102. So we have to assume that there is decimal point at the end of 71 

Then, 

71 x 102 ---------> 71. x 102

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

We have to move the decimal point to the left. 

Number of digits between the first non zero digit and the decimal point is 1.

So, the decimal point has to be moved 1 digit to the left and exponent of 10 should be 1 (positive integer)

71. x 102 = 7.1 x 101 x 102

71

Hence, the scientific notation of 71 x 102 is

7.1 x 103

Problem 4 :

Write the given number in scientific notation. 

33 x 10-3

Solution :

Here, we don't find decimal point in 33 x 10-3 So we have to assume that there is decimal point at the end of 33 

Then, 

33 x 10-3 ---------> 33. x 10-3 

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

We have to move the decimal point to the left. 

Number of digits between the first non zero digit and the decimal point is 1.

So, the decimal point has to be moved 1 digit to the left and exponent of 10 should be 1 (positive integer)

33. x 10-3  = 3.3 x 101 x 10-3

33. x 10-3  = 3.3 x 10-2

Hence, the scientific notation of 33 x 10-3 is

3.3 x 10-2

Problem 5 :

Write the given number in scientific notation. 

0.63 x 10-3

Solution : 

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

We have to move the decimal point to the right. 

Number of digits from the decimal point up to the first non zero digit is 1.

So, the decimal point has to be moved 1 digit to the right and exponent of 10 should be -1 (negative integer)

0.63 x 10-3  =  6.3 x 10-1 x 10-3

0.63 x 10-3  =  6.3 x 10-4

Hence, the scientific notation of 0.63 10-3 is

6.3 x 10-4

Problem 6 :

Write the given number in scientific notation. 

0.000216

Solution : 

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

We have to move the decimal point to the right. 

Number of digits from the decimal point up to the first non zero digit is 4.

So, the decimal point has to be moved 4 digits to the right and exponent of 10 should be -4 (negative integer)

0.000216   =  2.16 x 10-4

Hence, the scientific notation of 0.000216 is

2.16 10-4

Problem 7 :

Write the given number in scientific notation. 

0.0000009

Solution : 

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

We have to move the decimal point to the right. 

Number of digits from the decimal point up to the first non zero digit is 7.

So, the decimal point has to be moved 7 digits to the right and exponent of 10 should be -7 (negative integer)

0.0000009   =  9 x 10-7

Hence, the scientific notation of 0.0000009 is

10-7

Problem 8 :

Write the given number in scientific notation. 

804 x 102

Solution :

Here, we don't find decimal point in 804 x 102. So we have to assume that there is decimal point at the end . 

Then, 

804 x 102 ---------> 804. x 102

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

We have to move the decimal point to the left. 

Number of digits between the first non zero digit and the decimal point is 2.

So, the decimal point has to be moved 2 digits to the left and exponent of 10 should be 2 (positive integer)

804. x 102 =  8.04 x 102 x 102

804. x 102 =  8.04 x 104

Hence, the scientific notation of 804 x 102 is 

8.04 x 104

Problem 9 :

Write the given number in scientific notation. 

4.8

Solution :

Here, the given number is almost in scientific notation.

Because there is only one non zero digit before the decimal point.

We don't have to move the decimal point either to the left or right.

Then, exponent of 10 should be zero.

4.8  =  4.8 x 100

Hence, the scientific notation of 4.8 is

4.8 x 100

Problem 10 :

Write the given number in scientific notation. 

0.99 x 10

Solution : 

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

We have to move the decimal to the right. 

Number of digits from the decimal point up to the first non zero digit is 1.

So, the decimal point has to be moved 1 digit to the right and exponent of 10 should be -1 (negative integer)

0.99 x 101  =  9.9 x 10-1 x 101

0.99 x 101  =  9.9 x 10-1+1

0.99 x 10-1  =  9.9 x 100

Hence, the scientific notation of 0.99 10-1 is

9.9 x 100

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