Question 1

Solve.
-A computer compiles a program in 0.000885 seconds. Write this in scientific notation. 
A) $8.85 \times 10 ^ { 3 }$
B) $8.85 \times 10 ^ { - 4 }$
C) $8.85 \times 10 ^ { - 6 }$
D) $8.85 \times 10 ^ { - 5 }$

Accepted Answer

To convert 0.000885 to scientific notation, we move the decimal point 4 places to the right, making it $8.85 \times 10^{-4}$.

Question 2

Solve.
-If the mass of an object is $5.50756 \times 10 ^ { 3 }$ tons and its density is $6.28 \times 10 ^ { - 2 }$ tons per cubic foot, find the volume of this object. (Use the formula $\mathrm { D } = \frac { \mathrm { M } } { \mathrm { V } }$ and round to the nearest hundredth, if necessary.)
A) $8.77 \times 10 ^ { 3 }$ cubic feet
B) $8.77 \times 10 ^ { 4 }$ cubic feet
C) $8.77 \times 10 ^ { 5 }$ cubic feet
D) $87.7 \times 10 ^ { 4 }$ cubic feet

Accepted Answer

The volume $ V $ can be calculated using the formula $ V = \frac{M}{D} $. Substituting the given values, $ V = \frac{5.50756 \times 10^3}{6.28 \times 10^{-2}} \approx 8.77 \times 10^4 $ cubic feet.

Question 3

Write in decimal notation.
-$$2.0138 \times 10 ^ { - 7 }$$
A) $0.0000020138$
B) $0.000000020138$
C) $- 201380,000$
D) $0.00000020138$

Accepted Answer

The answer of Write in decimal notation.
-\[2.0138 \times 10 ^...

Question 4

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
-$$( 180,000,000 ) ( 0.00003 ) ( 2000 ) ( 0.003 )$$
A) $3.24 \times 10 ^ { 5 }$
B) $3.24 \times 10 ^ { 6 }$
C) $3.24 \times 10 ^ { 3 }$
D) $3.24 \times 10 ^ { 4 }$

Accepted Answer

The answer of Evaluate by using scientific notation and the...

Question 5

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
-$\frac { ( 5,000,000 ) ( 78,000 ) } { 39,000,000,000 }$
A) $1.0$
B) $1.0 \times 10 ^ { 1 }$
C) $1.0 \times 10 ^ { - 1 }$
D) $1.0 \times 2$

Accepted Answer

First, convert all numbers to scientific notation: $5,000,000 = 5 \times 10^6$, $78,000 = 7.8 \times 10^4$, $39,000,000,000 = 3.9 \times 10^{10}$. Then, $\frac{(5 \times 10^6)(7.8 \times 10^4)}{3.9 \times 10^{10}} = \frac{39 \times 10^{10}}{3.9 \times 10^{10}} = 10 = 1.0 \times 10^1$.

Question 6

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
-$( 0.0075 ) ( 0.0000008 ) ( 0.001 )$
A) $6.0 \times 10 ^ { - 12 }$
B) $6.0 \times 10 ^ { - 14 }$
C) $6.0 \times 10 ^ { - 11 }$
D) $6.0 \times 10 ^ { - 13 }$

Accepted Answer

Convert each number to scientific notation: $0.0075 = 7.5 \times 10^{-3}$, $0.0000008 = 8 \times 10^{-7}$, $0.001 = 1 \times 10^{-3}$. Multiply the coefficients: $7.5 \times 8 \times 1 = 60$. Add the exponents: $-3 + (-7) + (-3) = -13$. Combine: $60 \times 10^{-13} = 6.0 \times 10^{-12}$.

Question 7

Solve.
-The sun radiates energy into space at the rate of $3.9 \times 10 ^ { 26 }$ joules per second. How many joules are emitted in three weeks?
A) $7.07616 \times 10 ^ { 26 }$ joules
B) $7.07616 \times 10 ^ { 32 }$ joules
C) $7.07616 \times 10 ^ { 53 }$ joules
D) $7.07616 \times 10 ^ { 59 }$ joules

Accepted Answer

To find the total energy emitted in three weeks, multiply the rate of energy emission per second by the number of seconds in three weeks. There are $3 \times 7 \times 24 \times 60 \times 60 = 1,814,400$ seconds in three weeks. Therefore, the total energy emitted is $3.9 \times 10^{26} \times 1,814,400 = 7.07616 \times 10^{32}$ joules.

Question 8

Solve.
-A particle is observed moving at $2.18 \times 10 ^ { - 3 }$ meters per second. Find the distance the particle would travel in $1.82 \times 10 ^ { - 4 }$ seconds.
A) $3.97 \times 10 ^ { - 8 }$ meters
B) $0.40 \times 10 ^ { - 7 }$ meters
C) $3.97 \times 10 ^ { - 6 }$ meters
D) $3.97 \times 10 ^ { - 7 }$ meters

Accepted Answer

Distance = Speed × Time= $2.18 \times 10 ^ { - 3 }$ m/s × $1.82 \times 10 ^ { - 4 }$ s= $3.97 \times 10 ^ { - 7 }$ m

Question 9

Solve.
-Approximately $7 \times 10 ^ { 3 }$ employees of a certain company average $\$ 30,000$ each year in salary. What is the total amount earned by all the employees of this company per year? Write your answer in scientific notation.
A) $\$ 21 \times 10 ^ { 9 }$
B) $\$ 21 \times 10 ^ { 8 }$
C) $\$ 2.1 \times 10 ^ { 9 }$
D) $\$ 2.1 \times 10 ^ { 8 }$

Accepted Answer

The answer of Solve.
-Approximately \(7 \times 10 ^ { 3...

Question 10

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
-$$\frac { ( 0.00032 ) ( 0.0002 ) } { 0.0008 }$$
A) $8 \times 10 ^ { - 5 }$
B) $64 \times 10 ^ { - 6 }$
C) $8 \times 10 ^ { 5 }$
D) $64 \times 10 ^ { 6 }$

Accepted Answer

First, convert each number to scientific notation: $0.00032 = 3.2 \times 10^{-4}$, $0.0002 = 2 \times 10^{-4}$, $0.0008 = 8 \times 10^{-4}$. Then, $\frac{(3.2 \times 10^{-4})(2 \times 10^{-4})}{8 \times 10^{-4}} = \frac{6.4 \times 10^{-8}}{8 \times 10^{-4}} = 8 \times 10^{-5}$.

Question 11

Solve.
-The mass of an electron is approximately $9.11 \times 10 ^ { - 28 }$ grams. Find the mass of $260,000,000$ electrons.
A) $2.3686 \times 10 ^ { - 20 }$ grams
B) $2.3686 \times 10 ^ { - 18 }$ grams
C) $2.3686 \times 10 ^ { - 19 }$ grams
D) $2.3686 \times 10 ^ { - 17 }$ grams

Accepted Answer

To find the mass of 260,000,000 electrons, multiply the mass of one electron by 260,000,000: $9.11 \times 10^{-28} \times 260,000,000 = 2.3686 \times 10^{-19}$ grams.

Question 12

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
-$\frac { 12,000,000,000 } { 0.00002 }$
A) $6 \times 10 ^ { 14 }$
B) $10 \times 10 ^ { 13 }$
C) $10 \times 10 ^ { 14 }$
D) $6 \times 10 ^ { 13 }$

Accepted Answer

First, express both numbers in scientific notation: $12,000,000,000 = 1.2 \times 10^{10}$ and $0.00002 = 2 \times 10^{-5}$. Then, divide the two: $\frac{1.2 \times 10^{10}}{2 \times 10^{-5}} = 0.6 \times 10^{15} = 6 \times 10^{14}$.

Question 13

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
-$$( 0.00004 ) ^ { 3 }$$
A) $6.4 \times 10 ^ { - 13 }$
B) $6.4 \times 10 ^ { - 14 }$
C) $1.2 \times 10 ^ { - 14 }$
D) $6.4 \times 10 ^ { - 11 }$

Accepted Answer

The answer of Evaluate by using scientific notation and the...

Question 14

Solve.
-In a state with a population of 5,000,000 people, the average citizen spends $6,000 on housing each year. What is the total spent on housing for the state? Write your answer in scientific notation.
A) $\$ 30 \times 10 ^ { 11 }$
B) $\$ 3 \times 10 ^ { 10 }$
C) $\$ 30 \times 10 ^ { 10 }$
D) $\$ 3 \times 10 ^ { 9 }$

Accepted Answer

The total spent on housing is calculated by multiplying the population (5,000,000 or $5 \times 10^6$) by the average spending per citizen ($6,000 or $6 \times 10^3$). This gives $5 \times 10^6 \times 6 \times 10^3 = 30 \times 10^9$, which can be simplified to $\$ 3 \times 10 ^ { 10 }$.

Question 15

Solve.
-$$- 6 x ^ { 3 }$$
A) monomial, degree $- 6$
B) binomial, degree $- 6$
C) binomial, degree 3
D) monomial, degree 3

Accepted Answer

The given expression $-6x^3$ is a monomial because it consists of only one term, and its degree is 3, which is the exponent of the variable $x$.

Question 16

Solve.
-$- 9 x y ^ { 9 }$
A) monomial, degree is 1
B) monomial, degree 9
C) binomial, degree 10
D) monomial, degree 10

Accepted Answer

The answer of Solve.
-\(- 9 x y ^ { 9...

Question 17

Solve.
-$$- 9 x }$$
A) binomial, degree 0
B) monomial, degree $- 9$
C) monomial, degree 1
D) monomial, degree 0

Accepted Answer

The expression $-9x$ is a monomial because it consists of a single term. The degree of a monomial is the sum of the exponents of the variables in the term. Here, the variable $x$ has an exponent of 1, so the degree is 1.

Question 18

Solve.
-A computer compiles a program in $8.637 \times 10 ^ { - 6 }$ seconds. Write this in decimal notation.
A) $0.0000008637$
B) $0.00008637$
C) $- 8,637,000$
D) $0.000008637$

Accepted Answer

To convert $8.637 \times 10 ^ { - 6 }$ seconds from scientific notation to decimal notation, you move the decimal point 6 places to the left, resulting in $0.000008637$.

Question 19

Solve.
-If the mass of an object is $4.61825 \times 10 ^ { - 5 }$ tons and its volume is $7.25 \times 10 ^ { - 3 }$ cubic feet, find the density of this object. (Use the formula $D = \frac { M } { V }$ and round to the nearest hundredth, if necessary.)
A) $6.37 \times 10 ^ { - 2 }$ tons per cubic foot
B) $6.37 \times 10 ^ { - 3 }$ tons per cubic foot
C) $6.37 \times 10 ^ { - 4 }$ tons per cubic foot
D) $63.7 \times 10 ^ { - 3 }$ tons per cubic foot

Accepted Answer

The density $D$ is calculated using the formula $D = \frac{M}{V}$. Substituting the given values, $D = \frac{4.61825 \times 10^{-5}}{7.25 \times 10^{-3}}$. This simplifies to approximately $6.37 \times 10^{-3}$ tons per cubic foot.

Question 20

Solve.
-If the density of a substance is $5.21 \times 10 ^ { - 4 }$ tons per cubic foot, what would be the mass of $8.51 \times 10 ^ { - 3 }$ cubic feet of this substance. (Use the formula $D = \frac { M } { V }$ and round to the nearest hundredth, if necessary.)
A) $4.43 \times 10 ^ { - 7 }$ tons
B) $4.43 \times 10 ^ { - 6 }$ tons
C) $0.44 \times 10 ^ { - 6 }$ tons
D) $4.43 \times 10 ^ { - 5 }$ tons

Accepted Answer

To find the mass (M) of the substance, rearrange the formula to $M = D \times V$. Substituting the given values, $M = 5.21 \times 10^{-4} \times 8.51 \times 10^{-3}$. Multiplying these gives $M = 4.43 \times 10^{-6}$ tons.

Quiz 5: Exponents and Polynomials

Solve. -A computer compiles a program in 0.000885 seconds. Write this in scientific notation.

Solve. -If the mass of an object is $5.50756 \times 10 ^ { 3 }$ tons and its density is $6.28 \times 10 ^ { - 2 }$ tons per cubic foot, find the volume of this object. (Use the formula $\mathrm { D } = \frac { \mathrm { M } } { \mathrm { V } }$ and round to the nearest hundredth, if necessary.)

Write in decimal notation. - $2.0138 \times 10 ^ { - 7 }$

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - $( 180,000,000 ) ( 0.00003 ) ( 2000 ) ( 0.003 )$

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - $\frac { ( 5,000,000 ) ( 78,000 ) } { 39,000,000,000 }$

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - $( 0.0075 ) ( 0.0000008 ) ( 0.001 )$

Solve. -The sun radiates energy into space at the rate of $3.9 \times 10 ^ { 26 }$ joules per second. How many joules are emitted in three weeks?

Solve. -A particle is observed moving at $2.18 \times 10 ^ { - 3 }$ meters per second. Find the distance the particle would travel in $1.82 \times 10 ^ { - 4 }$ seconds.

Solve. -Approximately $7 \times 10 ^ { 3 }$ employees of a certain company average $\$ 30,000$ each year in salary. What is the total amount earned by all the employees of this company per year? Write your answer in scientific notation.

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - $\frac { ( 0.00032 ) ( 0.0002 ) } { 0.0008 }$

Solve. -The mass of an electron is approximately $9.11 \times 10 ^ { - 28 }$ grams. Find the mass of $260,000,000$ electrons.

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - $\frac { 12,000,000,000 } { 0.00002 }$

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - $( 0.00004 ) ^ { 3 }$

Solve. -In a state with a population of 5,000,000 people, the average citizen spends $6,000 on housing each year. What is the total spent on housing for the state? Write your answer in scientific notation.

Solve. - $- 6 x ^ { 3 }$

Solve. - $- 9 x y ^ { 9 }$

Solve. - $- 9 x }$

Solve. -A computer compiles a program in $8.637 \times 10 ^ { - 6 }$ seconds. Write this in decimal notation.

Solve. -If the mass of an object is $4.61825 \times 10 ^ { - 5 }$ tons and its volume is $7.25 \times 10 ^ { - 3 }$ cubic feet, find the density of this object. (Use the formula $D = \frac { M } { V }$ and round to the nearest hundredth, if necessary.)

Solve. -If the density of a substance is $5.21 \times 10 ^ { - 4 }$ tons per cubic foot, what would be the mass of $8.51 \times 10 ^ { - 3 }$ cubic feet of this substance. (Use the formula $D = \frac { M } { V }$ and round to the nearest hundredth, if necessary.)

Quiz 5: Exponents and Polynomials

Solve. -A computer compiles a program in 0.000885 seconds. Write this in scientific notation.

Write in decimal notation. - 2.0138×10−72.0138 \times 10 ^ { - 7 }2.0138×10−7

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - (180,000,000) (0.00003) (2000) (0.003) ( 180,000,000 ) ( 0.00003 ) ( 2000 ) ( 0.003 ) (180,000,000) (0.00003) (2000) (0.003)

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - (5,000,000) (78,000) 39,000,000,000\frac { ( 5,000,000 ) ( 78,000 ) } { 39,000,000,000 }39,000,000,000(5,000,000) (78,000) ​

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - (0.0075) (0.0000008) (0.001) ( 0.0075 ) ( 0.0000008 ) ( 0.001 ) (0.0075) (0.0000008) (0.001)

Solve. -The sun radiates energy into space at the rate of 3.9×10263.9 \times 10 ^ { 26 }3.9×1026 joules per second. How many joules are emitted in three weeks?

Solve. -A particle is observed moving at 2.18×10−32.18 \times 10 ^ { - 3 }2.18×10−3 meters per second. Find the distance the particle would travel in 1.82×10−41.82 \times 10 ^ { - 4 }1.82×10−4 seconds.

Solve. -Approximately 7×1037 \times 10 ^ { 3 }7×103 employees of a certain company average $30,000\$ 30,000$30,000 each year in salary. What is the total amount earned by all the employees of this company per year? Write your answer in scientific notation.

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - (0.00032) (0.0002) 0.0008\frac { ( 0.00032 ) ( 0.0002 ) } { 0.0008 }0.0008(0.00032) (0.0002) ​

Solve. -The mass of an electron is approximately 9.11×10−289.11 \times 10 ^ { - 28 }9.11×10−28 grams. Find the mass of 260,000,000260,000,000260,000,000 electrons.

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - 12,000,000,0000.00002\frac { 12,000,000,000 } { 0.00002 }0.0000212,000,000,000​

Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation. - (0.00004) 3( 0.00004 ) ^ { 3 }(0.00004) 3