CONVERT BETWEEN STANDARD AND SCIENTIFIC NOTATION WORKSHEET

Problem 1 :

Write the following number in scientific notation.

205852

Problem 2 :

Write the following number in scientific notation.

3449098.96

Problem 3 :

Write the following number in scientific notation.

0.00008035

Problem 4 :

Write the following number in standard form.  

5.236 x 105

Problem 5 :

Write the following numbers in standard form.

6.415 x 10-6

Problem 6 :

Write the following number in standard form.  

1.72 x 109

Problem 7 :

Write the following number in standard form.  

0.00023 x 107

Problem 8 :

Write the following number in standard form.

0.036 x 10-3

Solutions

Problem 1 :

Write the following number in scientific notation.

205852

Solution :

Here, we don't find decimal point in 205852. So we have to assume that there is decimal point at the end . 

Then,

205852 ---------> 205852.

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 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). 

Therefore, the scientific notation of 205852 is

2.05852 x 105

Problem 2 :

Write the following number in scientific notation.

3449098.96

Solution :

3449098.96

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 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)

Therefore, the scientific notation of 3449098.96 is

3.44909896 x 106

Problem 3 :

Write the following number in scientific notation.

0.00008035

Solution : 

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

We have to move the decimal point to the right. 

No. 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)

Therefore, the scientific notation of 0.00008035 is

8.035 x 10-5

Problem 4 :

Write the following number in standard form.  

5.236 x 105

Solution :

Here, the exponent of 10 is positive 5. So we have to move the decimal point five digits to the right.

In 5.236, we have only three digits after the decimal point.

So, we have to add two zeros to move the decimal point five digits to the right.   

Therefore, the standard form of 5.236 x 105 is 

523600

Problem 5 :

Write the following numbers in standard form.

6.415 x 10-6

Solution :

Here, the exponent of 10 is negative 6. So we have to move the decimal point six digits to the left.

In 6.415, we have only 1 digit before the decimal point.

So, we have to add five zeros to move the decimal point six digits to the left.   

Therefore, the standard form of 6.415 x 10-6 is 

0.000006415

Problem 6 :

Write the following number in standard form.  

1.72 x 109

Solution :

Here, the exponent of 10 is positive 9. So we have to move the decimal point nine digits to the right.

In 1.72, we have only two digits after the decimal point.

So, we have to add seven zeros to move the decimal point nine digits to the right.   

Therefore, the standard form of 1.72 x 109 is 

1720000000

Problem 7 :

Write the following number in standard form.  

0.00023 x 107

Solution :

Here, the exponent of 10 is positive 7. So we have to move the decimal point seven digits to the right.

In 0.00023, we have only five digits after the decimal point.

So, we have to add two zeros to move the decimal point seven digits to the right.   

Therefore, the standard form of 0.00023 x 107 is 

2300

Problem 8 :

Write the following numbers in standard form.

0.036 x 10-3

Solution :

Here, the exponent of 10 is negative 3. So we have to move the decimal point three digits to the left.

In 0.036, we don't have any non zero digit before the decimal point.

So, we have to add three zeros to move the decimal point three digits to the left.   

Therefore the standard form of 0.036 x 10-3 is 

0.000036

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