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Scientific Notation Worksheets - Page 19

Scientific Notation Worksheets
  • Page 19
 181.  
The mean distance from Venus to the Sun is about 1.08 × 109 km. Write this number in decimal form.
a.
180,000,000 km
b.
1,080,000,000 km
c.
108,000,000 km
d.
18,000,000 km


Solution:

1.08 × 109 = 1,080,000,000 km
[Multiplying by 1,000,000,000 moves the decimal point 9 places to the right.]

The mean distance from Venus to the Sun expressed in decimal form is 1,080,000,000 km.


Correct answer : (2)
 182.  
The 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


Solution:

9.87 × 108 = 987,000,000 acres
[Multiplying by 100,000,000 moves the decimal point 8 places to the right.]

The total extent of farm land expressed in decimal form is 987,000,000 acres.


Correct answer : (3)
 183.  
The lowest temperature in a lab setting is about 2.8 × 10 - 10 ok. Write this number in decimal form.
a.
0.0000000028 ok
b.
0.000000028 ok
c.
0.000000000028 ok
d.
0.00000000028 ok


Solution:

2.8 × 10 - 10 = 0.00000000028
[Multiplying by 0.0000000001 moves the decimal point 10 places to the left.]

The lowest temperature in a lab setting expressed in decimal form is 0.00000000028 ok.


Correct answer : (4)
 184.  
Simplify the product (7.6 × 108) (6.3 × 10-3) and write the result in scientific notation.
a.
4.788 × 105
b.
4.788 × 106
c.
47.880 × 106
d.
4.788


Solution:

(7.6 × 108) (6.3 × 10-3) = (7.6 × 6.3) (108 × 10-3)
[Use multiplication properties.]

= (47.88) (105)
[Use product of powers property.]

= (4.788 × 101) × 105
[Write 47.88 in scientific notation.]

= 4.788 × 106
[Use product of powers property.]


Correct answer : (2)
 185.  
Simplify:
(4 × 10- 9)2
a.
1.6 × 10- 18
b.
16 × 10- 1
c.
16 × 1018
d.
1.6 × 10- 17


Solution:

(4 × 10- 9)2 = 42 × (10- 9)2
[Use power of a product property.]

= 16 × 10-18
[Use power of a power property.]

= (1.6 × 101) × 10- 18
[Write 16 in scientific notation.]

= 1.6 × 10- 17
[Use product of powers property.]


Correct answer : (4)
 186.  
Write 950,000,000 in scientific notation.
a.
9.5 × 108
b.
9.5 × 106
c.
9.5 × 107
d.
9.5 × 109


Solution:

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.

The first factor in the scientific notation of 950,000,000 is 9.5.
[Move the decimal point to get a factor greater than 1 and less than 10.]

The second factor is 108.
[The decimal point moved 8 places to the left. Use this number as the exponent of 10.]

So, the scientific notation of 950,000,000 is 9.5 × 108.


Correct answer : (1)
 187.  
The speed of sound in air is 331 m/s at 0oC. Write the speed of sound in air in scientific notation.
a.
3.31 × 101 m/s
b.
0.331 × 102 m/s
c.
3.31 × 102 m/s
d.
3.31 × 103 m/s


Solution:

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.

The first factor in the scientific notation of 331 is 3.31.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 102.
[The decimal point is moved 2 places to the left. Use this number as the exponent of 10.]

The speed of sound in air in scientific notation is 3.31 × 102 m/s.


Correct answer : (3)
 188.  
The 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 square miles
b.
32,000 square miles
c.
3,200,000 square miles
d.
320,000 square miles


Solution:

3.2 × 104 = 32,000
[Multiplying by 10,000, moves the decimal point 4 places to the right.]

The total area occupied by the state of South Carolina in decimal form is 32,000 square miles.


Correct answer : (2)
 189.  
Express 333 × 10 - 3 in decimal form.
a.
333
b.
33.3
c.
0.333
d.
3.33


Solution:

As the exponent of 10 in the number is - 3, move the decimal point 3 places to the left.

So, the number in decimal form is 0.333.


Correct answer : (3)
 190.  
Express 9.673 × 106 in standard form.
a.
967,300
b.
96,730
c.
96,730,000
d.
9,673,000


Solution:

As the exponent of 10 in the number is 6, move the decimal point 6 places to the right.

9.673 × 106 = 9,673,000
[As there are only 3 digits after the decimal, insert 3 zeroes at the end.]


Correct answer : (4)

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