Elementary and Intermediate Algebra 5th

Alan S. Tussy, R. David Gustafson

Chapter 5

Exponents and Polynomials - all with Video Answers

Educators

Section 3

Scientific Notation

Problem 1

Fill in the blanks.
$4.84 \times 10^{5}$ is written in __________ notation. $484,000$ is written in ___________ notation.

Anastasios S.

Anastasios S.

Numerade Educator

Problem 2

Fill in the blanks.
$10^{3}, 10^{50},$ and $10^{-4}$ are ________ of 10

Anastasios S.

Numerade Educator

Problem 3

Fill in the blanks.
When we multiply a decimal by $10^{5},$ the decimal point moves 5 places to the __________When we multiply a decimal by $10^{-7}$, the decimal point moves 7 places to the _________.

Anastasios S.

Numerade Educator

Problem 4

Fill in the blanks.
Describe the procedure for converting a number from scientific notation to standard form.
a. If the exponent on the base of 10 is positive, move the decimal point the same number of places to the _______ as the exponent.
b. If the exponent on the base of 10 is negative, move the decimal point the same number of places to the _______ as the absolute value of the exponent.

Anastasios S.

Numerade Educator

Problem 5

Fill in the blanks.
a. When a real number greater than or equal to 10 is written in scientific notation, the exponent on 10 is a _______ integer.
b. When a real number between 0 and 1 is written in scientific notation, the exponent on 10 is a _______ integer.

Anastasios S.

Numerade Educator

Problem 6

Fill in the blanks.
The arrows show the movement of a decimal point. By what power of 10 was each decimal multiplied?
a. 0.0000000556
b. $8,04,1,000,000$

Rujula D.

Numerade Educator

Problem 7

Fill in the blanks to write number in scientific notation.
a. $7,700=\quad \times 10^{3}$
b. $500,000= \quad \times 10^{5}$
c. $114,000,000=1.14 \times 10$

Anastasios S.

Numerade Educator

Problem 8

Fill in the blanks to write number in scientific notation.
a. $0.0082=\quad \times 10^{-3}$
b. $0.0000001=\quad \times 10^{-7}$
c. $0.00003457=3.457 \times 10$

Anastasios S.

Numerade Educator

Problem 9

Write each expression so that the decimal numbers are grouped together and the powers of ten are grouped together.
a. $\left(5.1 \times 10^{9}\right)\left(1.5 \times 10^{22}\right)$
b. $\frac{8.8 \times 10^{30}}{2.2 \times 10^{19}}$

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Problem 10

Simplify each expression.
a. $10^{24} \times 10^{33}$
b. $\frac{10^{50}}{10^{36}}$
c. $\frac{10^{15} \times 10^{27}}{10^{40}}$

Anastasios S.

Numerade Educator

Problem 11

Fill in the blanks. A positive number is written in scientific notation when it is written in the form $N \times 10^{n},$ where $\quad\leq N<\quad$ and $n$ is an _________.

Rujula D.

Numerade Educator

Problem 12

Express each power of 10 in fraction form and decimal form.
a. $10^{-3}$
b. $10^{-6}$

Anastasios S.

Numerade Educator

Problem 13

Convert number to standard notation.
$2.3 \times 10^{2}$

Anastasios S.

Numerade Educator

Problem 14

Convert number to standard notation.
$3.75 \times 10^{4}$

Anastasios S.

Numerade Educator

Problem 15

Convert number to standard notation.
$8.12 \times 10^{5}$

Anastasios S.

Numerade Educator

Problem 16

Convert number to standard notation.
$1.2 \times 10^{3}$

Anastasios S.

Numerade Educator

Problem 17

Convert number to standard notation.
$1.15 \times 10^{-3}$

Anastasios S.

Numerade Educator

Problem 18

Convert number to standard notation.
$4.9 \times 10^{-2}$

Anastasios S.

Numerade Educator

Problem 19

Convert number to standard notation.
$9.76 \times 10^{-4}$

Anastasios S.

Numerade Educator

Problem 20

Convert number to standard notation.
$7.63 \times 10^{-5}$

Anastasios S.

Numerade Educator

Problem 21

Convert number to standard notation.
$6.001 \times 10^{6}$

Anastasios S.

Numerade Educator

Problem 22

Convert number to standard notation.
$9.998 \times 10^{5}$

Anastasios S.

Numerade Educator

Problem 23

Convert number to standard notation.
$2.718 \times 10^{0}$

Anastasios S.

Numerade Educator

Problem 24

Convert number to standard notation.
$3.14 \times 10^{0}$

Anastasios S.

Numerade Educator

Problem 25

Convert number to standard notation.
$6.789 \times 10^{-2}$

Anastasios S.

Numerade Educator

Problem 26

Convert number to standard notation.
$4.321 \times 10^{-1}$

Anastasios S.

Numerade Educator

Problem 27

Convert number to standard notation.
$2.0 \times 10^{-5}$

Anastasios S.

Numerade Educator

Problem 28

Convert number to standard notation.
$7.0 \times 10^{-6}$

Anastasios S.

Numerade Educator

Problem 29

Write number in scientific notation.
$23,000$

Anastasios S.

Numerade Educator

Problem 30

Write number in scientific notation.
$4,750$

Anastasios S.

Numerade Educator

Problem 31

Write number in scientific notation.
$1,700,000$

Anastasios S.

Numerade Educator

Problem 32

Write number in scientific notation.
$290,000$

Anastasios S.

Numerade Educator

Problem 33

Write number in scientific notation.
0.062

Anastasios S.

Numerade Educator

Problem 34

Write number in scientific notation.
0.00073

Anastasios S.

Numerade Educator

Problem 35

Write number in scientific notation.
0.0000051

Anastasios S.

Numerade Educator

Problem 36

Write number in scientific notation.
0.04

Rujula D.

Numerade Educator

Problem 37

Write number in scientific notation.
$5,000,000,000$

Anastasios S.

Numerade Educator

Problem 38

Write number in scientific notation.
$7,000,000$

Anastasios S.

Numerade Educator

Problem 39

Write number in scientific notation.
0.0000003

Anastasios S.

Numerade Educator

Problem 40

Write number in scientific notation.
0.0001

Anastasios S.

Numerade Educator

Problem 41

Write number in scientific notation.
$909,000,000$

Anastasios S.

Numerade Educator

Problem 42

Write number in scientific notation.
$7,007,000,000$

Anastasios S.

Numerade Educator

Problem 43

Write number in scientific notation.
0.0345

Anastasios S.

Numerade Educator

Problem 44

Write number in scientific notation.
0.000000567

Anastasios S.

Numerade Educator

Problem 45

Write number in scientific notation.
9

Anastasios S.

Numerade Educator

Problem 46

Write number in scientific notation.
2

Anastasios S.

Numerade Educator

Problem 47

Write number in scientific notation.
11

Anastasios S.

Numerade Educator

Problem 48

Write number in scientific notation.
55

Anastasios S.

Numerade Educator

Problem 49

Write number in scientific notation.
$1,718,000,000,000,000,000$

Rujula D.

Numerade Educator

Problem 50

Write number in scientific notation.
$44,180,000,000,000,000,000$

Anastasios S.

Numerade Educator

Problem 51

Write number in scientific notation.
0.0000000000000123

Rujula D.

Numerade Educator

Problem 52

Write number in scientific notation.
0.00000000000000000555

Rujula D.

Numerade Educator

Problem 53

Write number in scientific notation.
$73 \times 10^{4}$

Anastasios S.

Numerade Educator

Problem 54

Write number in scientific notation.
$99 \times 10^{5}$

Anastasios S.

Numerade Educator

Problem 55

Write number in scientific notation.
$201.8 \times 10^{15}$

Anastasios S.

Numerade Educator

Problem 56

Write number in scientific notation.
$154.3 \times 10^{17}$

Anastasios S.

Numerade Educator

Problem 57

Write number in scientific notation.
$0.073 \times 10^{-3}$

Anastasios S.

Numerade Educator

Problem 58

Write number in scientific notation.
$0.0017 \times 10^{-4}$

Anastasios S.

Numerade Educator

Problem 59

Write number in scientific notation.
$36.02 \times 10^{-20}$

Anastasios S.

Numerade Educator

Problem 60

Write number in scientific notation.
$56.29 \times 10^{-30}$

Anastasios S.

Numerade Educator

Problem 61

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\left(3.4 \times 10^{2}\right)\left(2.1 \times 10^{3}\right)$

Rujula D.

Numerade Educator

Problem 62

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\left(4.1 \times 10^{-3}\right)\left(3.4 \times 10^{4}\right)$

Rujula D.

Numerade Educator

Problem 63

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\left(8.4 \times 10^{-13}\right)\left(4.8 \times 10^{9}\right)$

Rujula D.

Numerade Educator

Problem 64

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\left(5.5 \times 10^{-15}\right)\left(2.2 \times 10^{13}\right)$

Rujula D.

Numerade Educator

Problem 65

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\frac{2.24 \times 10^{4}}{5.6 \times 10^{7}}$

Rujula D.

Numerade Educator

Problem 66

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\frac{2.47 \times 10^{5}}{3.8 \times 10^{-5}}$

Rujula D.

Numerade Educator

Problem 67

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\frac{9.3 \times 10^{2}}{3.1 \times 10^{-2}}$

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Problem 68

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\frac{7.2 \times 10^{6}}{1.2 \times 10^{8}}$

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Problem 69

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\frac{0.00000129}{0.0003}$

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Problem 70

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\frac{169,000,000,000}{26,000,000}$

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Problem 71

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
( 0.0000000056)$(5,500,000)$

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Problem 72

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
( 0.000000061)$(3,500,000,000)$

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Problem 73

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\frac{96,000}{(12,000)(0.00004)}$

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Problem 74

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\frac{(0.48)(14,400,000)}{96,000,000}$

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Problem 75

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\frac{2,475}{(132,000,000,000,000)(0.25)}$

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Problem 76

Use scientific notation to perform the calculations. Give all answers in scientific notation and standard notation.
$\frac{147,000,000,000,000}{(0.000049)(25)}$

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Problem 77

Find power.
$(456.4)^{6}$

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Numerade Educator

Problem 78

Find power.
$(0.009)^{-6}$

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Problem 79

Find power.
$225^{-5}$

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Numerade Educator

Problem 80

Find power.
$\left(\frac{1}{3}\right)^{-55}$

Rujula D.

Numerade Educator

Problem 81

The distance from Earth to Alpha Centauri (the nearest star outside our solar system) is about $25,700,000,000,000$ miles. Write this number in scientific notation.

Rujula D.

Numerade Educator

Problem 82

According to the U.S. Geological Survey, the total water supply of the world is $366,000,000,000,000,000,000$ gallons. Write this number in scientific notation.

Rujula D.

Numerade Educator

Problem 83

The surface area of Earth is $1.97 \times 10^{8}$ square miles, the surface area of the sun is $1.09 \times 10^{17}$ square miles, and the surface area of the moon is $1.46 \times 10^{7}$ square miles. Convert each number to standard notation.

Rujula D.

Numerade Educator

Problem 84

The number of atoms in 1 gram of iron is approximately $1.08 \times 10^{22} .$ Convert this number to standard notation.

Rujula D.

Numerade Educator

Problem 85

The mass of one grain of beach sand is approximately 0.00000000045 ounce. Write this number in scientific notation.

Rujula D.

Numerade Educator

Problem 86

The mass of a water molecule is approximately 0.000000000000000000001056 ounce. Write this number in scientific notation.

Rujula D.

Numerade Educator

Problem 87

Examples of the most common types of electromagnetic waves are given in the table in the next column. List the wavelengths in order from shortest to longest.
$\begin{array}{|l|l|l|}\hline \text { Type } & {\text { Use }} & {\text { Wavelength (in meters) }} \\ \hline \text { visible light } & {\text { lighting }} & {9.3 \times 10^{-6}} \\ \hline \text { infrared } & {\text { photography }} & {3.7 \times 10^{-5}} \\ \hline \text { x-ray } & {\text { photography }} & {2.7 \times 10^{-11}} \\ \hline \text { radio wave } & {\text { communication }} & {8.0 \times 10^{-14}} \\ \hline \text { gamma ray } & {\text { treating cancer }} & {8.9 \times 10^{-14}} \\ \hline \text { microwave } & {\text { cooking }} & {1.1 \times 10^{-2}} \\ \hline \text { ultraviolet } & {\text { sun lamp }} & {6.1 \times 10^{-8}} \\ \hline\end{array}$

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Problem 88

Exploration. On July $4,1997,$ the Pathfinder, carrying the rover vehicle called Sojourner, landed on Mars. The distance from Mars to Earth is approximately $3.5 \times 10^{7}$ miles. Use scientific notation to express this distance in feet.

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Problem 89

The speed of sound in air is approximately $3.3 \times 10^{4}$ centimeters per second. Use scientific notation to express this speed in kilometers per second. (Hint: 100 centimeters $=1$ meter and $1,000$ meters $=1$ kilometer.

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Problem 90

The mass of one proton is approximately $1.7 \times 10^{-24}$ gram. Use scientific notation to express the mass of 1 million protons.

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Problem 91

Light Years. One light year is about $5.87 \times 10^{12}$ miles. Use scientific notation to express this distance in feet.

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Problem 92

Oil. As of $2009,$ Saudi Arabia was believed to have crude oil reserves of about $2.65 \times 10^{11}$ barrels. A barrel contains 42 gallons of oil. Use scientific notation to express Saudi Arabia's oil reserves in gallons.

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Problem 93

As of June $2009,$ the total insured deposits in U.S. banks and savings and loans was approximately $7.6 \times 10^{12}$ dollars. If this money was invested at a rate of $4 \%$ simple annual interest, how much would it earn in 1 year? Use scientific notation to express the answer.

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Problem 94

As of December 2009 , the number of $\$ 20$ bills in circulation was approximately $6.4 \times 10^{9} .$ What was the total value of the currency? Express the answer in scientific notation and standard notation.

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Problem 95

In the United States, we use Latin prefixes in front of "illion" to name extremely large numbers. Write each number in scientific notation.
One million: $1,000,000$
One billion: $1,000,000,000$
One trillion: $1,000,000,000,000$
One quadrillion: $1,000,000,000,000,000$
One quintillion: $1,000,000,000,000,000,000$

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Numerade Educator

Problem 96

As of June 2009 , the world's fastest computer was the Cray Jaguar, owned by the Oak Ridge National Laboratory in Tennessee. If it could make $1.75 \times 10^{15}$ calculations in one second, how many could it make in one minute? Answer in scientific notation.

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Problem 97

In what situations would scientific notation be more convenient than standard notation?

Rujula D.

Numerade Educator

Problem 98

To multiply a number by a power of $10,$ we move the decimal point. Which way, and how far? Explain.

Rujula D.

Numerade Educator

Problem 99

$2.3 \times 10^{-3}$ contains a negative sign but represents a positive number. Explain.

Rujula D.

Numerade Educator

Problem 100

Explain why $237.8 \times 10^{8}$ is not written in scientific notation.

Rujula D.

Numerade Educator

Problem 101

If $y=-1,$ find the value of $-5 y^{55}$

Anastasios S.

Numerade Educator

Problem 102

What is the $y$ -intercept of the graph of $y=-3 x-5 ?$

Anastasios S.

Numerade Educator

Problem 103

Counseling. At the end of her first year of practice, a family counselor had 75 clients. At the end of her second year, she had 105 clients. If a linear trend continues, write an equation that gives the number of clients $c$ the counselor will have at the end of $t$ years.

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Problem 104

Is $(0,-5)$ a solution of $2 x+3 y \geq-14 ?$

Anastasios S.

Numerade Educator

Problem 105

Consider $2.5 \times 10^{-4} .$ Answer the following questions in scientific notation form.
a. What is its opposite?
b. What is its reciprocal?

Rujula D.

Numerade Educator

Problem 106

a. Write the numbers one million and one millionth in scientific notation.
b. By what number must we multiply one millionth to get one million?

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