Scientific Notation Chapter Questions
1. What is the purpose of scientific notation?
2. When would you use scientific notation?
3. How do you convert between standard form and scientific notation?
4. How do you compare numbers when they are written in scientific notation?
5. How do you multiply and divide numbers in scientific notation?
6. How do you add and subtract numbers in scientific notation?
Scientific Notation Chapter Problems
Purpose of Scientific Notation
Classwork
1. Express the following powers of ten in standard form:
a. 101 =
b. 102 =
c. 103 =
d. 104 =
e. 105 =
2. Express the following answers as powers of 10.
a. 103 x 105 =
b. 1011 x 106 =
c. 1012 x 10-8 =
d. 10-4 x 10-7 =
e. 10-9 x 103 =
Homework
3. Express the following powers of ten in standard form:
a. 109 =
b. 108 =
c. 107 =
d. 106 =
e. 105 =
4. Express the following answers as powers of 10.
a. 102 x 104 =
b. 103 x 1012 =
c. 10-6 x 108 =
d. 10-3 x 10-9 =
e. 10-7 x 102 =
How to Write Numbers in Scientific Notation
Classwork
5. Which of the following are correctly written in scientific notation?
a. 3.0 x 105
b. 0.56 x 109
c. 0.103 x 103
d. 15 x 10-5
e. 5.6 x 10-8
f. 4 x 102
g. 0.345 x 10-2
6. Write each number in scientific notation.
a. 13,030,000
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
418,000
25,024,000
4,500,000
20,000
870,000,000
0.0325
0.0000564
0.00092
0.001002
0.00006
0.00965784
7. Write each number in scientific notation.
a. Lightest blue whale: 418,000 lb
b. Thinnest glass: 0.00098 in.
c. Lightest bird egg: 0.0128 oz.
d. Diameter of thinnest copper wire: 0.0005 in.
e. Mass of Earth’s atmosphere: 5,700,000,000,000,000 tons
f. Amount of gold in Earth’s crust: 120,000,000,000,000 metric tons
Homework
8. Which of the following are correctly written in scientific notation?
a. 0.5 x 104
b. 15 x 109
c. 3.5567 x 10-7
d. 1 x 106
e. 5.04 x 10-4
f. 0.05 x 10-2
g. 6.788432 x 108
9. Write each number in scientific notation.
a. 4,566,000
b. 17,000,300
c. 35,000
d. 1,078,000,000
e. 4,560,700
f. 943,000,000,000
g. 0.000578
h. 0.004598732
i. 0.000000558744
j. 0.0001000358
k. 0.00045805
l. 0.000000000000851
10. Write each number in scientific notation.
a. Mass of smallest insect, a parasitic wasp: 0.00000492 g
b. Speed of light: 300,000,000 m/sec
c. Mass of a dust particle: 0.000000000753 kg
d. Distance from Earth to the Sun is approximately: 149,600,000 km
e. Earth’s circumference: 40,000,000 m
f. Distance between the Sun and Neptune: 4,497,100,000 km
Converting to Standard Form
Classwork
11. Write each number in standard form.
a. Temperature at the Sun’s core: 1.55 x 106 K
b. Lowest temperature ever in a lab: 2 x 10-11 K
c. Radius of the neon atom is about 3.5 x 10-11 meters
d. Radius of Earth’s orbit: 1.5 x 1011 meters
e. Avagadro’s number: 6.022 x 1023
f. Weight of a paper clip: 1.1 x 10-3 lb.
12. Write each number in standard form:
a. 7.5 x 105
b. 9.765 x 10-10
c. 1.27 x 10-8
d. 4.56 x 106
e. 3.0 x 10-6
f. 6.785168 x 108
g. 8.00045 x 10-4
Homework
13. Write each number in standard form.
a. Width of a human hair:7.5 x 10-5 meter
b. Distance between Jupiter and the Sun: 4.836 x 1011
c. Charge on a Proton/Electron: 1.602176 x 10-19 C
d. Faraday constant: 9.649 x 104
e. Number of bits on a computer hard disk (as of 2010): 1 x 1013 GB
f. Wavelength of green light: 5.5 x 10-7 m
14. Write each number in standard form:
a. 8.445 x 10-4
b. 5.256544 x 109
c. 1.0 x 10-5
d. 7.45207 x 108
e. 2.67 x 10-5
f. 6.0005 x 106
g. 4.00896 x 10-3
Comparing Numbers in Scientific Notation
Classwork
15. Place the appropriate inequality symbols between the following numbers:
a. 9.5 x 104
8.2 x 107
7
b. 6.231 x 10
2.34 x 103
c.
d.
e.
f.
g.
h.
i.
j.
4.567 x 10 -2
1.0 x 10-4
5.66 x 10-7
8.32 x 10-6
4.52 x 104
6.5431 x 108
3.5 x 10-6
4.509 x 1010
7.32 x 105
2.0 x 10-5
6.54 x 10-9
7.236 x 10-11
7.532 x 104
6.32 x 108
1.0 x 10-6
3.45 x 1010
16. Order the following sets of numbers from least to greatest.
a. 2.3 x 103
4.5 x 105
7.8 x 102
9
7
b. 4.0 x 10
5.0 x 10
6.0 x 1010
c. 4.3 x 104
7.5 x 10-2
1.9 x 106
-12
-25
d. 2.5 x 10
5.5 x 10
8.2 x 102
4
4
e. 5.4 x 10
3.2 x 10
9.9 x 104
f. 9.2 x 10-5
8.2 x 10-6
9.2 x 10-6
1.3 x 104
7.0 x 105
3.3 x 10-4
9.5 x 10-9
2.1 x 104
8.2 x 10-5
Homework
17. Place the appropriate inequality symbols between the following numbers:
a. 3.2 x 106
4.2 x 109
4
b. 5.41 x 10
6.54 x 107
-8
c. 9.875 x 10
1.0345 x 108
d. 3.0 x 10-6
4.0 x 10-9
-4
e. 4.35 x 10
7.21 x 10-3
-8
f. 8.369 x 10
4.1 x 10-13
6
g. 3.98 x 10
5.98 x 106
h. 1.65 x 104
1.56 x 104
-8
i. 8.3 x 10
3.0 x 10-8
15
j. 6.8999 x 10
7.43 x 1015
18. Order the following sets of numbers from least to greatest.
a. 4.7 x 103
8.9 x 107
6.5 x 105
b. 2.0 x 1012
3.0 x 106
4.0 x 108
5
-3
c. 9.9 x 10
5.7 x 10
1.8 x 10-7
-10
-6
d. 1.9 x 10
3.6 x 10
9.7 x 103
8
8
e. 9.3 x 10
5.0 x 10
8.9 x 108
f. 5.5 x 10-7
4.5 x 10-7
9.0 x 10-7
6.7 x 104
5.0 x 103
4.4 x 106
4.5 x 10-23
6.7 x 108
2.7 x 10-7
Multiplying and Dividing with Scientific Notation
Classwork
19. Evaluate the following. Express the result in scientific notation.
a. (3.0 x 10-5)(2.0 x 109)=
b. (4.0 x 103)(5.0 x 105)=
c. (6.0 x 10-5)(3.0 x 108)=
d. (1.5 x 108)(3.2 x 10-4)=
e. (2.7 x 10-3)(1.1 x 108)=
f. (1.3 x 10-4)(2.0 x 10-6)=
g. (8.4 x 106)÷(2.0 x 103)=
h. (9.3 x 108)÷(3.0 x 10-2)=
i. (5.4 x 1010)÷(2.0 x 104)=
j.
k.
l.
7.35𝑥 105
2.1𝑥108
4.5𝑥105
=
=
9.0𝑥109
3.6𝑥10−8
6.0𝑥10−12
=
20. A tiny space inside a computer chip has been measured to be 2.56 x 10-6 meters wide, 1.4 x 10-7
meters long, and 2.75 x 10-4 meters high. What is its volume?
21. In one year about 478 billion telephone calls were placed by 145 million United States telephone
subscribers. What was the average number of calls placed per subscriber?
Homework
22. Evaluate the following. Express the result in scientific notation.
a. (3.0 x 10-5)(3.0 x 108)=
b. (4.0 x 102)(4.0 x 107)=
c. (7.0 x 10-3)(6.0 x 106)=
d. (1.2 x 107)(2.2 x 10-3)=
e. (2.0 x 10-4)(7.1 x 109)=
f. (4.4 x 10-7)(3.0 x 10-3)=
g. (6.6 x 108)÷(2.0 x 104)=
h. (2.7 x 106)÷(3.0 x 10-4)=
i. (7.5 x 1012)÷(2.0 x 105)=
j.
k.
l.
6.6𝑥105
3.3𝑥1015
5.4𝑥104
=
=
9.0𝑥108
4.8𝑥10−4
8.0𝑥10−10
=
23. A tiny space inside another computer chip has been measured to be 3.5 x 10-7 meters wide, 1.8 x 10-8
meters long, and 6.45 x 10-5 meters high. What is its volume?
24. The point on a pin has a diameter of approximately 1 x 10-4 meters. If a neon atom has a diameter of
about 7.0 x 10-11 meters, about how many neon atoms could fit across the diameter of the point of a
pin?
Adding and Subtracting with Scientific Notation
Classwork
25. Evaluate the following. Express the result in scientific notation.
a. (2.1 x 105) + (2.7 x 105)=
b. (3.7 x 108) + (4.6 x 108)=
c. (6.8 x 10-6) - (3.4 x 10-6)=
d. (6.1 x 106) + (3.5 x 107)=
e. (8.5 x 1010) - (1.5 x 109)=
26. What is the difference between the mass of Earth (5.98 x 1024 kg) and the mass of Venus (4.87 x 1024
kg)?
27. What is the difference between the mass of Jupiter (1.90 x 10 27 kg) and the mass of Saturn (5.69 x
1026 kg)?
Homework
28. Evaluate the following. Express the result in scientific notation.
a. (5.8 x 109) + (3.1 x 109)=
b. (3.5 x 106) + (5.8 x 106)=
c. (7.5 x 10-4) - (4.2 x 10-4)=
d. (5.4 x 107) + (2.2 x 108)=
e. (6.5 x 1012) - (3.4 x 1011)=
29. What is the difference between the mass of Mars (6.42 x 1023 kg)and the mass of Mercury (3.3 x 1023
kg)?
30. What is the difference between the mass of Earth (5.98 x 1024 kg) and the mass of Mars (6.42 x 1023
kg)?
Answer Key
1.
a.
b.
c.
d.
e.
10
100
1000
10000
100000
a.
b.
c.
d.
e.
108
1017
104
10-11
10-6
a.
b.
c.
d.
e.
1000000000
100000000
10000000
1000000
100000
2.
3.
4.
a. 106
b. 1015
c. 102
d. 10-12
e. 10-5
5. A, E, F
6.
a. 1.303 x 107
b. 4.18 x 105
c. 2.5024 x 107
d. 4.5 x 106
e. 2 x 104
f. 8.7 x 108
g. 3.25 x 10-2
h. 5.64 x 10.5
i. 9.2 x 104
j. 1.002 x 10-3
k. 6 x 105
l. 9.65784 x 10-3
7.
a. 4.18 x 105
b. 9.8 x 10-4
c. 1.28 x 10.2
d. 5 x 10/4
e. 5.7 x 1015
f. 1.2 x 1014
8. C, D, E, G
9.
a. 4.566 x 106
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
1.70003 x 107
3.5 x 104
1.078 x 109
4.5607 x 106
9.43 x 1011
5.78 x 10-4
4.598732 x 10-3
5.58744 x 10-7
1.000358 x 10-11
4.5805 x 10-4
8.51 x 10-13
a.
b.
c.
d.
e.
f.
4.92 x 10-6
3 x 108
7.53 x 10-10
4.486 x 108
4 x 107
4.4971 x 109
a.
b.
c.
d.
e.
f.
1550000
.00000000002
.000000000035
150000000000
603300000000000000000
.0011
a.
b.
c.
d.
e.
f.
g.
750000
.0000000009765
.0000000127
4560000
.000003
678516800
.000800045
a.
b.
c.
d.
e.
f.
.000075
483600000000
.0000000000000000001602176
96490
10000000000000
.06000055
a.
b.
c.
d.
e.
f.
g.
.0008445
5256544000
.00001
745207000
.0000267
6000500
.00400896
10.
11.
12.
13.
14.
15.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
<
>
<
>
>
>
<
>
>
>
a.
b.
c.
d.
e.
f.
7.8 x 102, 2.3 x 103, 1.3 x 104, 4.5 x 105
7.0 x 105, 5.0 x 107, 4.0 x 109, 6.0 x 1010
3.3 x 10-4, 7.5 x 10-2, 4.3 x 104, 1.9 x 106
5.5 x 10-25, 2.5 x 10-12, 9.5 x 10-9, 8.2 x 102
2.1 x 104, 3.2 x 104, 5.4 x 104, 9.9 x 104
8.2 x 10-6, 9.2 x 10-6, 8.2 x 10-5, 9.2 x 10-5
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
<
<
<
>
<
>
<
>
>
<
a.
b.
c.
d.
e.
f.
4.7 x 103, 6.7 x 104, 6.5 x 105, 8.9 x 107
5.0 x 103, 3.0 x 106, 4.0 x 108, 2.0 x 1012
1.8 x 10-7, 5.7 x 10-3, 9.9 x 105, 4.4 x 106
4.5 x 10-23, 1.9 x 10-10, 3.6 x 10-6, 9.7 x 103
5.0 x 108, 6.7 x 108, 8.9 x 108, 9.3 x 108
2.7 x 10-7, 4.5 x 10-7, 5.5 x 10-7, 9.0 x 10-7
16.
17.
18.
19.
a. 6 x 104
b. 2 x 109
c. 1 x 108
d. 4.8 x 104
e. 2.97 x 105
f. 2.6 x 10-10
g. 4.2 x 103
h. 3.1 x 1010
i. 2.7 x 106
j. 3.5 x 10-3
k. 5 x 10-5
l. 6 x 103
20. 2.856 x 10-17
21. 3.296 x 103
22.
a. 9 x 103
b. 1.6 x 1010
c. 4.2 x 104
d. 2.64 x 104
e. 1.42 x 106
f. 1.32 x 10-9
g. 3.3 x 104
h. 9 x 109
i. 3.75 x 107
j. 2 x 10-10
k. 6 x 10-5
l. 6 x 105
23. 4.0635 x 10-19
24. 1.428571 x 106
25.
a. 4.8 x 105
b. 8.3 x 108
c. 3.4 x 10-6
d. 4.11 x 107
e. 8.35 x 1010s
26. 1.2 x 1024
27. 1.331 x 1027
28.
a. 8.9 x 109
b. 9.3 x 106
c. 3.3 x 10-4
d. 2.74 x 108
e. 6.16 x 1012
29. 3.12 x 1023
30. 5.338 x 1024