Kuta Software - Infinite Algebra 1
Name___________________________________
Operations With Scientific Notation
Date________________ Period____
Simplify. Write each answer in scientific notation.
−3
−3
1)  1.08 × 10  9.3 × 10 
−4
−1
2)  2 × 10  8.1 × 10 
−6
−5
3)  2.32 × 10  4 × 10 
3
4
4)  3.48 × 10  9.8 × 10 
−5
−6
5)  7.1 × 10  6.7 × 10 
3
0
6)  6 × 10  9.91 × 10 
7)
9)
11)
7.1 × 10 6
8)
8.2 × 10 1
4 × 10
4
3.63 × 10 −4
8.42 × 10
10)
3
5 × 10 2
4
13)  8.9 × 10 5 
12)
5.4 × 10 −1
3.4 × 10 1
9 × 10
−5
9.24 × 10 −6
8.9 × 10
6
8.4 × 10 6
−6
14)  4 × 10 −5 
-1-
−5
15)  6 × 10 
3
−5
17)  5.21 × 10 
19)
21)
23)
25)
3 × 10
−2
8 × 10
−1
2
16)  6.3 × 10 
2
−2
2.22 × 10 1
6 × 10
4.1 × 10
−3
22)
−5
1.62 × 10 −6
5.3 × 10 6
−5
−5
24)  8.8 × 10 
−2
4
26)  3.5 × 10  9 × 10 
8.08 × 10 −2
27)  8.8 × 10 2  2.25 × 10 −2 
4
4
1.28 × 10
5 × 10 −4
3.59 × 10
−5
18)  2.4 × 10 
20)
1.91 × 10 3
−6
28)
1.18 × 10 −4
3 × 10
-2-
0
Kuta Software - Infinite Algebra 1
Name___________________________________
Operations With Scientific Notation
Date________________ Period____
Simplify. Write each answer in scientific notation.
−3
−3
1)  1.08 × 10  9.3 × 10 
−4
−1
2)  2 × 10  8.1 × 10 
1.004 × 10 −5
−6
−5
3)  2.32 × 10  4 × 10 
9.28 × 10
1.62 × 10 −4
3
4
4)  3.48 × 10  9.8 × 10 
−11
−5
−6
5)  7.1 × 10  6.7 × 10 
3.41 × 10
3
0
6)  6 × 10  9.91 × 10 
4.757 × 10 −10
7)
7.1 × 10
6
8.2 × 10
1
5.946 × 10 4
8)
4 × 10
10)
−4
8.42 × 10
1
9 × 10
−5
9.24 × 10
1.102 × 10 8
5 × 10
−1
1.588 × 10 −2
4
3.63 × 10
11)
5.4 × 10
3.4 × 10
8.659 × 10 4
9)
−6
9.74 × 10 0
3
12)
2
8
8.9 × 10
6
8.4 × 10
6
1.684 × 10 1
1.06 × 10 0
4
−5
14)  4 × 10 
5
13)  8.9 × 10 
6.274 × 10 23
−6
2.441 × 10 26
-1-
−5
15)  6 × 10 
2.16 × 10
3
−13
−5
17)  5.21 × 10 
2.714 × 10
19)
3 × 10
−2
8 × 10
−1
21)
5 × 10
1.599 × 10
2
−9
3.318 × 10
3.59 × 10
3
1.62 × 10
22)
5.3 × 10
6
−5
24)  8.8 × 10 
−5
1
20
−3
−2
4
26)  3.5 × 10  9 × 10 
−3
8.08 × 10
9
3.057 × 10 −13
−2
1.617 × 10
25)
−19
−6
1.895 × 10
6 × 10
4
−5
3.203 × 10
2.22 × 10
−17
4
−2
3.82 × 10 6
23)
4.1 × 10
1.28 × 10
−4
−6
−5
18)  2.4 × 10 
20)
3.75 × 10
1.91 × 10
2
16)  6.3 × 10 
−2
3.15 × 10
3
7.426 × 10 −2
2
−2
27)  8.8 × 10  2.25 × 10 
1.98 × 10
28)
1.18 × 10
3 × 10
1
−4
0
3.933 × 10
-2-
−5
Mathematics 9
Unit 5 - Powers and Roots
Scientific Notation Worksheet
1.
2.
3.
Convert each of the following numbers to scientific notation.
(a.)
23 419
(b.)
-2.3419
(c.)
63x10x10
(d.)
(e.)
7.83
(f.)
0.23 x 10-9
(g.)
-0.003736 (h.)
0.00037
40.976
Identify the smallest and the largest number for each of the sets of
numbers below.
(a.)
2.3 x 10, -1.0 x 10-2, 1.0 x 10-2 and 2.3 x 100
(b.)
9.9 x 10-20, -1.7 x 10-1, 5.2 x 1020 and -4.1 x 1020
(c.)
-4.295, 6.5 x 10-4, 0.00068, and -4.3 x 100
Solve the following expressions involving numbers written in scientific
notation. Be sure to express your final answer in scientific notation as well.
(a.)
(3.0 x 104) x (1.0 x 102)
(b.)
(7.046 x 103) + (4.681 x 103)
(c.)
(6.1 x 102) - (4.38 x 104)
(d.)
(5.6 x 10-4) x (4.2 x 100)
(e.)
(-4.8 x 106) ÷ (1.2 x 103)
(f.)
(12 x 10-2) - (4.9 x 10-4)
(g.)
(9.9 x 10-18) + (4.2 x 10-19)
(h.)
(1.02 x 10-5) ÷ (3.05 x 10-9)
Convert to scientific notation back to standard form.
1
8.14 × 10 -1 =
2
9.37 × 10 1 =
3
3.36 × 10 1 =
4
4.11 × 10 4 =
5
9.17 × 10 4 =
6
9.3 × 10 2 =
7
2.63 × 10 3 =
8
5.98 × 10 1 =
9
7.5 × 10 1 =
10
5.77 × 10 4 =
11
6.04 × 10 4 =
12
4.69 × 10 0 =
13
2.52 × 10 2 =
14
5.02 × 10 4 =
15
9.38 × 10 2 =
16
8.84 × 10 4 =
17
7.23 × 10 2 =
18
3.35 × 10 0 =
19
3.96 × 10 1 =
20
2.55 × 10 1 =
21
2.06 × 10 5 =
22
8.93 × 10 2 =
23
1.93 × 10 1 =
24
5 × 10 -1 =
25
3.03 × 10 1 =
26
3.75 × 10 1 =
27
1.29 × 10 1 =
28
6.12 × 10 5 =
29
1.21 × 10 1 =
30
2.07 × 10 0 =
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Algebra - Scientific Notation
Name: _____________________________
Period: _______ Date: ___________
Write each number in Standard Notation (3 points each).
1. 2.35 × 105
2. 1.01 × 10−4
3. 9.9995 × 106
Write each number in Scientific Notation (3 points each).
4. 77,000,000
5. 565,482,000,000
6. 0.00000040
Order the numbers in each list from least to greatest (3 points each).
7. 4.5 × 1015 , 4.7 × 1014 , 2.9 × 1015 , 9.99 × 1014
_________________________________________________________________
8. 4.8 × 10−6 , 6.5 × 10−4 , 5.01 × 10−8 , 9.99 × 10−5
_________________________________________________________________
Simplify. Write each number using Scientific Notation (3 points each).
9. 5(7 × 105 )
10. 5(25 × 108 )
11. 0.5(7 × 10 −2 )
12. Is 18 × 10 −2 written in scientific notation? Explain your answer (3 points).
13. Explain why scientific notation is particularly helpful to astronomers who study distances among objects in
space (4 points).
Algebra Worksheet
Name: _____________________________
Scientific Notation
Period: _______ #: ______
Write each number in Standard Notation.
1. 7 × 10 4
2. 5.71 × 10−5
3. 31.3 × 106
Write each number in Scientific Notation.
4. 51,000,000
5. 975,000,000,000
6. 0.00000012
Order the numbers in each list from least to greatest.
7. 7 × 106 , 6 × 10 4 , 7 × 107 , 9 × 108
_________________________________________________________________
8. 4.8 × 10−6 , 6.5 × 10−4 , 5.01 × 10−8 , 9.99 × 10−5
_________________________________________________________________
9. 0.53 × 103 , 5300 × 10−2 , 5.3 × 105 , 530 × 108
(hint: convert each to correct scientific notation)
_________________________________________________________________
Simplify. Write each number using Scientific Notation.
10. 4(3 × 105 )
11. 5(5 × 10 4 )
12. 5(7 × 10 −2 )
13. 7(9 × 106 )
14. 0.2(3 × 102 )
15. 6(5.3 × 10 −4 )
.
1. Write 976,000 in scientific notation.
2. Write in standard form: 990 × 10 −3
3. Write in scientific notation: 0.00000040
[A] 4.0 × 10−6
[B] 4.0 × 10−5
[C] 40 × 10−6
[D] 4.0 × 10−7
4. Write in standard notation: 552
. × 109
[A] 5,520,000,000
[B] 552,000,000
[C] 55,200,000,000
[D] 0.00000000552
5. What is 510,000 in scientific notation?
[A] 51
. × 106
[B] 51
. × 10−5
[C] 51
. × 10−4
[D] 51
. × 105
6. Describe the process you would use to write 3,100,000 in scientific notation.
7. Is 18 × 10 −2 written in scientific notation? Explain your answer.
8.
Monarch’s Annual Cost to a Nation (U. S. $)
Country
Cost
United Kingdom
$9,500,000
Spain
$6,500,000
Denmark
$5,500,000
Belgium
$5,000,000
Netherlands
$5,000,000
Norway
$2,500,000
Sweden
$2,500,000
The table above shows the annual amount each nation spends on its monarch. What is the
annual cost of the monarch in Belgium expressed in scientific notation?
9. The table below shows a list of prefixes that are used with base units such as meter or
gram. Rewrite each of the factors in the table using powers of 10. For example, kilo means
Prefix
Multiply the root by
giga - 1,000,000,000
mega 1,000,000
kilo -
1,000 or 103 , so one kilometer is 1,000 meters.
1,000
hecto -
100
deka -
10
deci -
0.1
centi -
0.01
milli -
0.001
micro -
0.000001
nano 0.000000001
Source: Chemistry , Prentice Hall, 1989
10. Complete the following.
(a) The prefix tera means 1012 . How many grams are in three teragrams?
(b) The prefix pico means 0.000 000 000 001. Write this number as a power of ten.
11. Explain how to read 3.2 2 , and then write in standard form.
12. Write two numbers in exponential form that are between the values of 4 2 and 4 3 .
13. Which of the following is NOT written in scientific notation?
[A] 143.6 × 10−2
[B] 3.689 × 105
[C] 2.6 × 10−2
[D] 9.651 × 102
14. Which of the following is NOT equivalent to 0.095?
[A] 0.95 × 10 −1
[B] 0.00095 × 102
[C] 9.5 × 102
[D] 9.5 × 10 −2
15. Choose the standard form for 5.33 .
[A] 15.9
[B] 142
[C] 159
[D] 148.877
16. Evaluate the expression 4(15
. + 35
. )3.
[A] 500
[B] 60
[C] 50
[D] 800
17. The masses of four objects were measured during a physics experiment. The first and
the last both had a mass of 41.918 g. The second and the third objects both had a mass of
24.83 g. Find the total mass of the four objects. Write your answer in scientific notation.
18. Explain why scientific notation is particularly helpful to astronomers who study
distances among objects in space.
19. Write a letter to a classmate explaining how to write 62,000,000 in scientific notation.
20. In comparing two numbers expressed in scientific notation, can one assume that the
number with the greater exponent is automatically the larger number? Provide evidence for
your answer.
21. The diameter of Mercury, the smallest planet of the solar system, is about 31
. × 103
miles. The diameter of Jupiter, the largest planet, is about 8.8 × 104 miles. What is the
difference between the diameters of these planets expressed in scientific notation?
22. Which of the following numbers has the greatest value?
[A] 1111
. × 105
[B] 9.9 × 104
[C] 812
. × 103
[D] 6.5 × 104
Mathematics 9
Unit 5: Powers and Roots
Worksheet
Scientific Notation
Name:______________
1.
2.
Calculate each of the answers below. Make sure your final answer is in scientific
notation.
A)
(3.2 x 103) + (4.52 x 103)
B)
(6.5 x 10-4) + (9.7 x 10-4)
C)
(3.267 x 107) – (2.4 x 107)
D)
(4.56 x 10-5) – (3.2 x 10-5)
Calculate each of the answers below. Remember when adding and subtracting you must
have the same exponent.
A)
(3.5 x 10-3) + (6.25 x 10-5)
B)
(4.67 x 104) + (2.56 x 108)
C)
(4.67 x 10-2) + (7.89 x 105)
D)
(2.53 x 106) + (3.00 x 106)
E)
(9.23 x 10-4) – (5.67 x 10-7)
F)
(2.5 x 105) – (7.68 x 109)
G)
(7.86 x 10-5) – (4.35 x 109)
H)
(6.5 x 10-2) – (3.0 x 10-3)
3.
A computer is advertised as offering 25 gb of storage (gb refers to gigbytes). How many
bytes of storage is this? When personal computers first came on the market, a memory
of 180 kb was considered quite a large storage capacity. The new advertised computer
could replace the storage of how many of the early computers?
4.
The diameter of an electron is approximately 0.000 000 000 000 56 cm.
A)
How big would it look under a magnification of 120 000 000?
B)
Do you think we would be able to see it? Explain.
5.
A leaky faucet drips at a rate of one drop every 4 seconds. One drop of water is about
0.07 mL. Suppose that in the city of Halifax there are 3000 homes that have leaky
faucets.
A)
Calculate the amount of water wasted in a year?
B)
Write your answer in scientific notation.
C)
What are your assumptions?
Convert into Scientific notation.
1
0.817 =
2
106 =
3
0.479 =
4
9,210 =
5
9.93 =
6
56,600 =
7
58.5 =
8
237 =
9
81.6 =
10
629 =
11
0.951 =
12
772 =
13
6.43 =
14
0.483 =
15
53.9 =
16
0.00338 =
17
910 =
18
32.5 =
19
46.6 =
20
8.49 =
21
0.611 =
22
3,970 =
23
7,210 =
24
0.0214 =
25
8.53 =
26
4.46 =
27
61.9 =
28
0.00319 =
29
31,200 =
30
0.00111 =
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