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Scientific Notation Worksheets - Page 20

Scientific Notation Worksheets
  • Page 20
 191.  
Express 7.6 × 10- 5 in standard form.
a.
0.0000076
b.
0.000076
c.
0.00076
d.
0.0076


Solution:

7.6 × 10- 5 = 0.000076
[Since the exponent of 10 is - 5, move the decimal point 5 places to the left.]

So, the decimal form of 7.6 × 10- 5 is 0.000076.


Correct answer : (2)
 192.  
Rewrite the number 0.00006 using scientific notation.
a.
0.6 × 10- 5
b.
6 × 105
c.
6 × 10- 4
d.
6 × 10- 5


Solution:

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.

The first factor in the scientific notation of 0.00006 is 6.
[Move decimal point 5 places to the right to get a factor between 1 and 10.]

The second factor is 10- 5.
[As the decimal point is moved 5 places to the right, take exponent of 10 as - 5.]

So, the scientific notation of 0.00006 is 6 × 10- 5.


Correct answer : (4)
 193.  
Express 4,000,000 in scientific notation.
a.
4 × 107
b.
4 × 105
c.
4
d.
4 × 106


Solution:

A number is expressed in scientific notation as a product of two factors. The first one is a number between 1 and 10 and the second factor is an exponent of 10.

The first factor is 4.
[Move the decimal point 6 places to the left to get a number between 1 and 10.]

The second factor is 106.
[As the decimal is moved 6 places to the right, take 6 as exponent of 10.]

So, 4,000,000 can be written in scientific notation as 4 × 106.


Correct answer : (4)
 194.  
Simplify 0.66×1043.3×10- 4 and write the result in scientific notation.
a.
0.2 × 107
b.
2.0 × 104
c.
2.0 × 108
d.
2.0 × 107


Solution:

0.66×1043.3×10- 4 = (0.66 / 3.3) × 10410- 4
[Write as a product.]

= 0.2 × (108)
[Use quotient of powers property.]

= (2.0 × 10- 1) × 108
[Write 0.2 in scientific notation.]

= 2.0 × 107
[Use product of powers property.]


Correct answer : (4)
 195.  
Simplify 2.0×10- 96×10- 4 and write the result in scientific notation.
a.
3.3 × 106
b.
3.3 × 10- 6
c.
- 3.3 × 106
d.
- 3.3 × 10- 6


Solution:

2.0×10- 96×10- 4 = (2.0 / 6) × 10- 910- 4
[Write as a product.]

= 0.33 × 10- 5
[Use quotient of powers property.]

= (3.3 × 10- 1) × 10- 5
[Write 0.33 in scientific notation.]

= 3.3 × 10- 6
[Use product of powers property.]


Correct answer : (2)
 196.  
The mean distance of the Earth from the Moon is about 384,400 km. Write the distance in scientific notation.
a.
1.922 × 105 km
b.
3.844 × 105 km
c.
3844 km
d.
0.3844 × 105 km


Solution:

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.

The first factor in the scientific notation of 384,400 is 3.844.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 105.
[The decimal point is moved 5 places to the left. Use this number as the exponent of 10.]

The mean distance of the Earth from the Moon in scientific notation is about 3.844 × 105 km.


Correct answer : (2)
 197.  
The total men in the Civilian Labor Force in the U.S in the year 2001 was about 7.5743 × 107. Write the number in decimal form.
a.
7,574,300
b.
757,430
c.
75,743,000
d.
757,430,000


Solution:

7.5743 × 107 = 75,743,000
[Multiplying by 10,000,000, moves the decimal point 7 places to the right.]

The total men in the Civilian Labor Force in decimal form is 75,743,000.


Correct answer : (3)
 198.  
Multiply 7 × 107 and 5 × 10- 2. Express the result in scientific notation.
a.
3.5 × 106
b.
3.5
c.
35
d.
3.5 × 105


Solution:

= 7 × 5 × 107 × 10- 2
(7 × 107 ) × (5 × 10- 2 )
[Use commutative property of multiplication.]

= 35 × 107 × 10- 2
[Multiply 7 and 5.]

= 35 × 105
[Add exponents.]

= 3.5 × 101 × 105
[Write 35 = 3.5 × 101 in scientific notation.]

= 3.5 × 106
[Add exponents.]


Correct answer : (1)
 199.  
Express 760,000,000,000 in scientific notation.
a.
7.6 × 109
b.
7.6 × 108
c.
7.6 × 1011
d.
7.6 × 1010


Solution:

760,000,000,000
[Move the decimal point 11 places to the left, to get a factor greater than or equal to 1 and less than 10.]

= 7.6 × 100,000,000,000

= 7.6 × 1011
[The exponent of 10 is 11.]

The scientific notation of the number 760,000,000,000 is 7.6 × 1011.


Correct answer : (3)

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