CONVERT BETWEEN STANDARD AND SCIENTIFIC NOTATION WORKSHEET

Problems 1-5 : Write the given number in scientific notation.

Problem 1 :

205852

Problem 2 :

3449098.96

Problem 3 :

0.00008035

Problem 4 :

23.5007

Problem 5 :

0.003

Problems 5-10 : Write the given number in standard form.

Problem 6 :

5.236 x 10⁵

Problem 7 :

6.415 x 10^-6

Problem 8 :

1.72 x 10⁹

Problem 9 :

0.00023 x 10⁷

Problem 10 :

0.036 x 10^-3

Answers

1. Answer :

205852

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. 

Number of digits between the 1^st non zero digit and the decimal point is five.

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

2. Answer :

3449098.96

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 1^st non zero digit and the decimal point is six.

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

3. Answer :

0.00008035

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 five.

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

4. Answer :

23.5007

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 1^st non zero digit and the decimal point is one.

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

Therefore, the scientific notation of 23.5007 is

2.35007 x 10¹

5. Answer :

0.003

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 three.

So, the decimal point has to be moved 3 digits to the right and exponent of 10 should be -3 (negative integer)

Therefore, the scientific notation of 0.003 is

3.0 x 10^-3

6. Answer :

5.236 x 10⁵

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

7. Answer :

6.415 x 10^-6

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

8. Answer :

1.72 x 10⁹

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

9. Answer :

0.00023 x 10⁷

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

10. Answer :

0.036 x 10^-3

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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