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Scientific Notation Worksheets - Page 13

Scientific Notation Worksheets
  • Page 13
 121.  
Identify 5.849 × 106 in standard form.
a.
5849
b.
584900
c.
58490
d.
5849000


Solution:

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

5.849 × 106 = 5849000
[As there are only 3 digits after the decimal, insert 3 zeroes at the end.]


Correct answer : (4)
 122.  
Write 5.4 × 10-5 in standard form.
a.
0.00054
b.
0.000054
c.
0.0054
d.
54000.0


Solution:

5.4 x 10-5 = 0.000054
[Since the exponent of 10 is -5, move decimal point 5 places to left.]

So, the standard form of 5.4 x 10-5 is 0.000054.


Correct answer : (2)
 123.  
Express 80000000 in scientific notation.
a.
8 × 108
b.
8 × 107
c.
8
d.
8 × 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 8.
[Move the decimal point 7 places to the left to get a number between 0 and 10.]

The second factor is 107.
[As the decimal is moved 7 places to the right, take 7 as exponent of 10.]

So, 80000000 can be written in scientific notation as 8 × 107.


Correct answer : (2)
 124.  
Solve the expression (7.3 × 103) (4.3 × 104) and express the result in scientific notation.
a.
3.139 x 106
b.
3.139
c.
3.139 x 107
d.
3.139 x 108


Solution:

(7.3 x 103) (4.3 x 104) = (7.3 x 4.3) (103 x 104)
[Use multiplication properties.]

= 31.39 x 107
[Use product of powers property.]

= (3.139 x 101) x 107
[Write 31.39 in scientific notation.]

= 3.139 x 108
[Use product of powers property.]


Correct answer : (4)
 125.  
Solve (5.9 × 107) (6.5 × 10-5) and write the result in scientific notation.
a.
3.835
b.
3.835 x 103
c.
3.835 x 10-3
d.
3.835 x 102


Solution:

(5.9 x 107) (6.5 x 10-5) = (5.9 x 6.5) (107 x 10-5)
[Use multiplication properties.]

= (38.35) (102)
[Use product of powers property.]

= (3.835 x 101) x 102
[Write 38.35 in scientific notation.]

= 3.835 x 103
[Use product of powers property.]


Correct answer : (2)
 126.  
Simplify (0.34 × 104) / (3.4 × 10-4) and write the result in scientific notation.
a.
1.0 x 108
b.
1.0 x 10-7
c.
-1.0 x 107
d.
1.0 x 107


Solution:

(0.34 x 104) / (3.4 x 10-4) = (0.34 / 3.4) x (104 / 10-4)
[Write as a product.]

= 0.1 x (108)
[Use quotient of powers property.]

= (1.0 x 10-1) x 108
[Write 0.1 in scientific notation.]

= 1.0 x 107
[Use product of powers property.]


Correct answer : (4)
 127.  
Simplify (2.0 × 10-13) / (10 × 10-9) and write the result in scientific notation.
a.
2 x 105
b.
-2 x 105
c.
2 x 10-5
d.
-2 x 10-5


Solution:

(2.0 x 10-13) / (10 x 10-9) = (2.0 / 10) x (10-13 / 10-9)
[Write as a product.]

= 0.2 x 10-4
[Use quotient of powers property.]

= (2 x 10-1) x 10-4
[Write 0.2 in scientific notation.]

= 2 x 10-5
[Use product of powers property.]


Correct answer : (3)
 128.  
Simplify:
(7 × 10-7)2
a.
4.9 × 1013
b.
- 4.9 × 1013
c.
4.9 × 10- 13
d.
- 4.9 × 10- 13


Solution:

(7 × 10-7)2 = 72 × (10-7)2
[Use power of a product property.]

= 49 × 10-14
[Use power of a power property.]

= (4.9 × 101) × 10-14
[Write 49 in scientific notation.]

= 4.9 × 10-13
[Use product of powers property.]


Correct answer : (3)
 129.  
Write 83972 in scientific notation.
a.
839.72 x 1016
b.
83.972 x 104
c.
83.972
d.
8.3972 x 104


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 is 8.3972.
[Move the decimal point such that the number is between 1 and 10.]

The second factor is 104.
[As the decimal is moved 4 places to the left, take the exponent of 10 as 4.]

So, the number 83972 in scientific notation is 8.3972 x 104.


Correct answer : (4)
 130.  
A teacher asked four students to evaluate 5 × 104. Sunny answered 5000, Jeff answered 50000, Andy answered 500000, and William answered 5000000. Who among the four was correct?
a.
Andy
b.
William
c.
Jeff
d.
Sunny


Solution:

5 x 104 = 5 x 10000
[Evaluate power.]

= 50000
[Multiply 5 and 10000.]

So, Jeff is correct.


Correct answer : (3)

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