Solved Examples and Worksheet for Converting Numbers to Standard and Scientific Notation

Q1The population of Delaware was 783,600 in the year 2000. Express the number in scientific notation.

A. 7.836 × 104
B. 7.836 × 105
C. 7.836 × 103
D. 7.836 × 106

Solutions
Share 
Step: 1
A number is written in scientific notation as the product of two factors. The first factor should be greater than 1 and less than 10 and the second factor should be a power of 10.
Step: 2
The first factor in the scientific notation of 783,600 is 7.836.
  [Move the decimal point to get a factor greater than or equal to 1 and less than 10.]
Step: 3
The second factor is 105.
  [The decimal is moved 5 places to the left. Use this number as the exponent of 10.]
Step: 4
The population of Delaware in scientific notation is 7.836 × 105.
Correct Answer is :   7.836 × 105
Q2The mean distance from the Pluto to the Sun is about 5,913,520,000 km. Write this number in scientific notation.
A. 5.91352 × 108 km
B. 5.91352 × 1010 km
C. 5.91352 × 107 km
D. 5.91352 × 109 km

Solutions
Share 
Step: 1
A number in scientific notation is written as the product of two factors. The first factor is an integer between 1 and 10 and the second factor is an exponent of 10.
Step: 2
The first factor in the scientific notation of 5,913,520,000 is 5.91352.
  [Move the decimal point to get a factor greater than or equal to 1 and less than 10.]
Step: 3
The second factor is 109.
  [The decimal is moved 9 places to the left. Use this number as the exponent of 10.]
Step: 4
So, the mean distance from the Pluto to the Sun in scientific notation is 5.91352 × 109 km.
Correct Answer is :   5.91352 × 109 km
Q3The radius of a circle is 0.004 meters. Identify this number in scientific notation.
A. 4 × 10- 4 meters
B. 4 × 10- 3 meters
C. 4 × 103 meters
D. 4 × 10- 2 meters

Solutions
Share 
Step: 1
A number in scientific notation is represented as the product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.
Step: 2
The first factor in the scientific notation of 0.004 is 4.
  [Move the decimal point to get a factor greater than or equal to 1 and less than 10.]
Step: 3
The second factor is 10- 3.
  [The decimal point is moved 3 places to the right. The negative of this number is used as the exponent of 10.]
Step: 4
The radius of the circle in scientific notation is 4 × 10- 3 meters.
Correct Answer is :   4 × 10- 3 meters
Q4The diameter of a cable is 2.68 × 10-3 meters. Identify the standard form.

A. 2,680
B. 0.000268
C. 0.00268
D. 0.268

Solutions
Share 
Step: 1
2.68 × 10-3 = 0.00268
  [Multiplying by 0.001 moves the decimal point 3 places to the left.]
Step: 2
The diameter of the cable in standard notation is 0.00268 meters.
Correct Answer is :   0.00268
Q5Convert 62834 to scientific notation.
A. 628.34 x 1014
B. 6.2834 x 104
C. 62.834
D. 62.834 x 104

Solutions
Share 
Step: 1
A number is expressed in scientific notation as a product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.
Step: 2
The first factor is 6.2834.
  [Move the decimal point such that the number is between 1 and 10.]
Step: 3
The second factor is 104.
  [As the decimal is moved 4 places to the left, take the exponent of 10 as 4.]
Step: 4
So, the number 62834 in scientific notation is 6.2834 x 104.
Correct Answer is :   6.2834 x 104
Q6An elephant weighs 1400 kg. Convert its weight to scientific notation.

A. 1.4 x 103
B. 1.4 x 104
C. 14 x 10-3
D. 1.4

Solutions
Share 
Step: 1
A number is expressed in scientific notation as the product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.
Step: 2
The first factor is 1.4.
  [Move the decimal point such that the number is greater than 1 but less than 10.]
Step: 3
The second factor is 103.
  [As the decimal is moved 3 places to the left, take the exponent of 10 as 3.]
Step: 4
So, the number 1400 in scientific notation is 1.4 x 103.
Correct Answer is :   1.4 x 103
Q7The total number of farms in the year 2000 was about 3,428,000. Convert this number to scientific notation.

A. 3.428 × 107
B. 3.428 × 105
C. 3.428 × 106
D. None of the above

Solutions
Share 
Step: 1
A number in scientific notation is a product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.
Step: 2
The first factor in the scientific notation of 3,428,000 is 3.428.
  [Move the decimal point to get a factor greater than or equal to 1 and less than 10.]
Step: 3
The second factor is 106.
  [The decimal point is moved 6 places to the left. Use this number as the exponent of 10.]
Step: 4
The total number of farms in scientific notation is 3.428 × 106.
Correct Answer is :   3.428 × 106
Q8The total number of farms in the year 2000 in the U.S was about 1,514,000. Write the number in scientific notation.
A. 1.514 × 104
B. 1.514 × 105
C. 1.514 × 106
D. 1.514 × 107

Solutions
Share 
Step: 1
A number in scientific notation is a product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.
Step: 2
The first factor in the scientific notation of 1,514,000 is 1.514.
  [Move the decimal point to get a factor greater than or equal to 1 and less than 10.]
Step: 3
The second factor is 106.
  [The decimal point is moved 6 places to the left. Use this number as the exponent of 10.]
Step: 4
The total number of farms in scientific notation is 1.514 × 106.
Correct Answer is :   1.514 × 106
Q9The total area occupied by the state of South Carolina is about 3.2 × 104 square miles. Write the number in decimal form.

A. 3,200,000 square miles
B. 320,000 square miles
C. 3,200 square miles
D. 32,000 square miles

Solutions
Share 
Step: 1
3.2 × 104 = 32,000
  [Multiplying by 10,000, moves the decimal point 4 places to the right.]
Step: 2
The total area occupied by the state of South Carolina in decimal form is 32,000 square miles.
Correct Answer is :   32,000 square miles
Q10The total extent of farm land in U.S is about 9.87 × 108 acres. Write this number in decimal form.

A. 9,870,000 acres
B. 989,000,000 acres
C. 987,000,000 acres
D. 978,000,000 acres

Solutions
Share 
Step: 1
9.87 × 108 = 987,000,000 acres
  [Multiplying by 100,000,000 moves the decimal point 8 places to the right.]
Step: 2
The total extent of farm land expressed in decimal form is 987,000,000 acres.
Correct Answer is :   987,000,000 acres
Q11The mean distance from the Jupiter to the Sun is about 483 × 106 miles. Express the number in standard form.
A. 1,787,000,000 miles
B. 142,000,000 miles
C. 256,000,000 miles
D. 483,000,000 miles

Solutions
Share 
Step: 1
483 × 106 = 483,000,000 miles
  [Shift the decimal point 6 places to the right.]
Step: 2
The mean distance from Jupiter to the Sun expressed in standard form is 483,000,000 miles.
Correct Answer is :   483,000,000 miles
Q12The height of the Eiffel Tower located in Paris is 986 ft. Express the height in scientific notation.

A. 9.86 × 102 ft
B. 9.86 × 103 ft
C. 9.86 × 104 ft
D. 9.68 × 102 ft

Solutions
Share 
Step: 1
A number in scientific notation is the product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.
Step: 2
The first factor in the scientific notation of 986 is 9.86.
  [Shift the decimal point to get a factor greater than or equal to 1 and less than 10.]
Step: 3
The second factor is 102.
  [Use the number of places the decimal point shifts as the exponent of 10.]
Step: 4
So, the height of the Empire state building in scientific notation is 9.86 × 102 ft.
Correct Answer is :   9.86 × 102 ft
Q13The height of the Willis Tower located in Chicago is 1,454 ft. Express the height in scientific notation.

A. 1.454 × 102 ft
B. 1.454 × 103 ft
C. 1.544 × 103 ft
D. 1.454 × 104 ft

Solutions
Share 
Step: 1
A number in scientific notation is the product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.
Step: 2
The first factor in the scientific notation of 1,454 is 1.454.
  [Shift the decimal point to get a factor greater than or equal to 1 and less than 10.]
Step: 3
The second factor is 103.
  [Use the number of places the decimal point shifts as the exponent of 10.]
Step: 4
So, the height of the Willis Tower in scientific notation is 1.454 × 103 ft.
Correct Answer is :   1.454 × 103 ft
Q14The diameter of an hydrogen atom is about 0.00000000011 meters. What is this number in scientific notation?
A. 0.11 × 10-9
B. 11 × 10-11
C. 1.1 × 10-10
D. 1.1 × 109

Solutions
Share 
Step: 1
A number in scientific notation is the product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.
Step: 2
The first factor in the scientific notation of 0.00000000011 is 1.1.
  [Move the decimal point to get a factor greater than or equal to 1 and less than 10.]
Step: 3
The second factor is 10-10.
  [The decimal point moved 10 places to the right. The negative of this number is used as the exponent of 10.]
Step: 4
The diameter of an hydrogen atom expressed in scientific notation is 1.1 × 10- 10 meters.
Correct Answer is :   1.1 × 10-10
Q15The mean distance from the Mercury to the Sun is about 5.79 × 107 km. Which of the following is the standard form of the number?

A. 0.0000579
B. 57,900,000
C. 579,000,000
D. 5,790,000,000

Solutions
Share 
Step: 1
5.79 × 107 = 57900000 km
  [Multiplying by 10,000,000 moves the decimal point 7 places to the right.]
Step: 2
The mean distance from Mercury to the Sun expressed in standard form is 57,900,000 km.
Correct Answer is :   57,900,000

HighSchool Math