CONVERTING SCIENTIFIC NOTATION TO STANDARD FORM WORKSHEET

Write each of the following numbers in standard form.

Problem 1 :

2.5 x 10²

Problem 2 :

1.9 x 10^-2

Problem 3 :

5.236 x 10⁵

Problem 4 :

6.415 x 10^-6

Problem 5 :

1.72 x 10⁹

Problem 6 :

2.3 x 10^-7

Problem 7 :

3.6 x 10⁴

Problem 8 :

2.05852 x 10⁵

Problem 9 :

3.44909896 x 10⁶

Problem 10 :

8.035 x 10^-5

Problem 11 :

A person can do 2.563 units of a certain work in a minute. Find the total number of units of the same work the person can do in 10³ minutes.

Problem 12 :

A man walks 7.5 miles of distance in 10² minutes. Find the speed of the man in miles per minute.

Answers

1. Answer :

2.5 x 10²

Since the exponent of 10 is positive 2, the decimal point has to be shifted to the right by two digits.

In 2.5, there is only one digits to right of the decimal point.

So, we have to add one zero to move the decimal point to the right by two digits.   

Therefore, the standard form of 2.5 x 10² is

250

2. Answer :

1.9 x 10^-2

Since the exponent of 10 is negative 2, the decimal point has to be shifted to the left by two digits.

In 2.5, there is only one digits to left of the decimal point.

So, we have to add one zero to move the decimal point to the left by two digits.   

Therefore, the standard form of 1.9 x 10^-2 is

0.019

3. Answer :

5.236 x 10⁵

Since the exponent of 10 is positive 5. the decimal point has to be shifted to the right by five digits

In 5.236, there are only three digits to right of the decimal point.

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

Therefore, the standard form of 5.236 x 10⁵ is 

523600

4. Answer :

6.415 x 10^-6

Since the exponent of 10 is negative 6. the decimal has to  be shifted to the left by six digits.

In 6.415, we have only 1 digit to the left of the decimal point.

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

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

0.000006415

5. Answer :

1.72 x 10⁹

Since the exponent of 10 is positive 9, the decimal point has to be shifted to the right by nine digits.

In 1.72, we have only two digits to the right of the decimal point.

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

Therefore, the standard form of 1.72 x 10⁹ is 

1720000000

6. Answer :

2.3 x 10^-7

Since the exponent of 10 is negative 7, the decimal point has to be shifted to the left by seven digits.

In 2.3, we have only one digit to the left of the decimal point.

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

Therefore, the standard form of 2.3 x 10^-7 is 

0.00000023

7. Answer :

3.6 x 10⁴

Since the exponent of 10 is positive 4, the decimal point has to be shifted to the right by four digits.

In 3.6, we have only one digit to the right of the decimal point.

So, we have to add three zeros to move the decimal point to the right by four digits.

Therefore the standard form of 3.6 x 10⁴ is 

36000

8. Answer :

2.05852 x 10⁵

Since the exponent of 10 is positive 5, the decimal point has to be shifted to the right by five digits.

In 2.05852, we have five digits to the right of the decimal point.

So, we don't have to add zeros and we can move the decimal point to the right by five digits.

Therefore, the standard form of 2.05852 x 10⁵ is 

205852

9. Answer :

3.44909896 x 10⁶

Since the exponent of 10 is positive 6, the decimal point has to be shifted to the right by six digits.

In 3.44909896, we have eight digits to the right of the decimal point.

So, we don't have to add zeros and we can move the decimal point to the right by six digits.

Therefore, the standard form of 3.44909896 x 10⁶ is 

3449098.96

10. Answer :

8.035 x 10^-5

Since the exponent of 10 is negative 5, the decimal point has to be shifted to the left by five digits.

In 8.035, we have only one digit to the left of the decimal point.

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

Therefore, the standard form of 8.035 x 10^-5 is

0.00008035

11. Answer :

Number of units work completed in 1 minute :

= 2.563

Total number of units of the same work completed in 10³ minutes.

= 2.563 x 10³

Since the exponent of 10 is positive 3, the decimal point has to be shifted to the right by three digits.

In 2.563, we have three digits to the right of the decimal point.

So, we don't have to add zeros and we can move the decimal point to the right by three digits.

= 2563 units

12. Answer :

Formula for speed :

speed = distance ÷ time

Substitute distance = 7.5 and time = 10².

= 7.5 ÷ 10³

= 7.5 x 10^-3

Since the exponent of 10 is negative 3, the decimal point has to be shifted to the left by three digits.

In 7.5, we have only one digit to the left of the decimal point.

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

= 0.0075 miles

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