Question 1

Convert the given number to scientific notation.
-0.000014914

Accepted Answer

To convert to scientific notation, we need to move the decimal point until there is one non-zero digit to the left of it. In this case, we need to move the decimal point 5 places to the right:
0.000014914 = 1.4914 × 10^-5

Question 2

Convert the given number to scientific notation.
-1,037,000,000,000,000

Accepted Answer

The number is very large, so it needs to be expressed in scientific notation with a positive exponent. The correct form is obtained by moving the decimal point 15 places to the left, giving $ 1.037 $, and then multiplying by $ 10^{15} $ to account for the decimal shift. Therefore, the answer is choice A.

Question 3

Solve the problem. Express your answer in scientific notation, and round to one decimal place.
-A computer can do one calculation in 1.4 × 10-7 seconds. How long would it take the computer to do a million (106) calculations?

Accepted Answer

The answer of Solve the problem. Express your answer in...

Question 4

Solve the problem. Express your answer in scientific notation, and round to one decimal place.
-In a state with a population of 7,000,000 people, the average citizen spends $6,000 on housing each year. What is the total spent on housing for the state?

Accepted Answer

The total spent on housing is calculated by multiplying the population (7,000,000) by the average spending per citizen ($6,000), which equals $42,000,000,000 or $4.2 	imes 10^{10} in scientific notation.

Question 5

Perform the indicated calculation. Express your answer using scientific notation.
-$$\left( 9.24 \times 10 ^ { 5 } \right) \div \left( 4.4 \times 10 ^ { - 6 } \right)$$

Accepted Answer

To divide two numbers in scientific notation, we need to divide the significant figures and subtract the exponents. Therefore, we have
$$ \frac{ 9.24 	imes 10 ^ { 5 } }{ 4.4 	imes 10 ^ { - 6 } } = \frac{ 9.24 }{ 4.4 } 	imes 10 ^ { 5 - ( -6 ) } = 2.1 	imes 10^{11} $$
Therefore, the answer is choice C) $2.1 	imes 10^{11}$.

Question 6

Perform the indicated calculation. Express your answer using scientific notation.
-$$\left( 6.6 \times 10 ^ { - 3 } \right) \left( 7.4 \times 10 ^ { 8 } \right)$$

Accepted Answer

To multiply two numbers written in scientific notation, we first multiply the two decimal parts and then add the exponents.

$$ \left( 6.6 \times 10 ^ { - 3 } \right) \left( 7.4 \times 10 ^ { 8 } \right) = 6.6 \cdot 7.4 \times 10^{-3+8} = 48.84 \times 10 ^ 5 = 4.884 \times 10 ^ { 6 } $$

Therefore, the answer is C.

Question 7

Perform the indicated calculation. Express your answer using scientific notation.
-$$( 6,350,000,000 ) \div ( 2,318,000 )$$

Accepted Answer

Dividing $6,350,000,000$ by $2,318,000$ gives $2737.19806763...$, which is approximately $2.74 \times 10^3$ in scientific notation.

Question 8

Perform the indicated calculation. Express your answer using scientific notation.
-$\left( 15 \times 10 ^ { - 5 } \right) \div \left( 3 \times 10 ^ { 4 } \right)$

Accepted Answer

To divide powers of 10, subtract the exponent in the denominator from the exponent in the numerator. 
So, we have: $$\left( 15 	imes 10 ^ { - 5 } ight) \div \left( 3 	imes 10 ^ { 4 } ight) =  \frac{15}{3} 	imes 10 ^ {-5} \div 10^4 = 5 	imes 10^{-5-4} = 5 	imes 10 ^ {-9}$$
Therefore, the answer is choice C.

Question 9

Convert the given number to scientific notation.
-0.0000000381018

Accepted Answer

To convert a number to scientific notation, we move the decimal point to the right or left until there is only one non-zero digit to the left of the decimal point. Then, the coefficient is multiplied by 10 raised to the number of places the decimal point was moved. In this case, we move the decimal point 8 places to the right to get 3.81018 and the exponent is -8 since we moved the decimal point to the left. Thus, the answer is 3.81018 x 10^-8.

Question 10

Perform the indicated calculation. Express your answer using scientific notation.
-$\left( 1.9 \times 10 ^ { - 7 } \right) \left( 1.6 \times 10 ^ { - 4 } \right)$

Accepted Answer

To multiply numbers in scientific notation, multiply the coefficients and add the exponents.

\begin{align*}
\left( 1.9 	imes 10 ^ { - 7 } ight) \left( 1.6 	imes 10 ^ { - 4 } ight) &= (1.9 \cdot 1.6) 	imes 10^{(-7 - 4)} \
&= 3.04 	imes 10^{-11}
\end{align*}

Therefore, the answer is choice B.

Question 11

Convert the given number to scientific notation.
-0.000000215019

Accepted Answer

To convert 0.000000215019 to scientific notation, we move the decimal point 7 places to the right, making it $2.15019 \times 10^{-7}$.

Question 12

Convert the given number to scientific notation.
-1,086,000,000,000,000,000

Accepted Answer

To convert to scientific notation, we want to write the number in the form $a \times 10^n$ where $1 \leq a < 10$ and $n$ is an integer. We can do this by moving the decimal point 18 places to the left to obtain $1.086 \times 10^{18}$. Since the decimal point moved to the left, the exponent should be positive.

Question 13

Convert the given number to scientific notation.
-0.000009447

Accepted Answer

To convert a number to scientific notation, we need to first move the decimal point so that there is only one non-zero digit to the left of it. In this case, we can move the decimal point 6 places to the right to get 0.000009447 = 9.447 × 10⁻⁶. Therefore, the correct choice is C.

Question 14

Convert the given number to scientific notation.
-83,000,000

Accepted Answer

To convert the number to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. In this case, we get 8.3. We then count the number of decimal places we moved the decimal point to the left, which is 7. Therefore, the answer is 8.3 x 10^7.

Question 15

Perform the indicated calculation. Express your answer using scientific notation.
-$$\left( 15.64 \times 10 ^ { 3 } \right) \div \left( 4 \times 10 ^ { - 5 } \right)$$

Accepted Answer

The answer of Perform the indicated calculation. Express your answer...

Question 16

Perform the indicated calculation. Express your answer using scientific notation.
-$( 0.0000000064 ) ( 160,000,000,000 )$

Accepted Answer

To multiply these numbers in scientific notation, first convert them: $0.0000000064 = 6.4 \times 10^{-9}$ and $160,000,000,000 = 1.6 \times 10^{11}$. Multiplying these gives $6.4 \times 1.6 = 10.24$, and $(-9) + 11 = 2$, so $10.24 \times 10^{2}$, which simplifies to $1.024 \times 10^{3}$, or approximately $1.02 \times 10^{3}$.

Question 17

Solve the problem. Express your answer in scientific notation, and round to one decimal place.
-The speed of light is 1.86 × 105 miles/second. How far can light travel in one year? Round to one decimal place.

Accepted Answer

To calculate how far light can travel in one year, we need to multiply its speed by the number of seconds in a year. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year.

1 year = 365 days = 365 x 24 hours = 365 x 24 x 60 minutes = 365 x 24 x 60 x 60 seconds

So,

Distance light can travel in one year = speed of light x time

= 1.86 x 105 miles/second x (365 x 24 x 60 x 60 seconds)

= 1.86 x 105 miles/second x 31,536,000 seconds

= 5.878 x 1012 miles

Rounding to one decimal place gives us 5.9 x 1012 miles, which is choice B.

Question 18

Solve the problem. Express your answer in scientific notation, and round to one decimal place.
-The mass of an electron is approximately $9.11 \times 10 ^ { - 28 }$ grams. Find the mass of $813,000,000$ electrons.

Accepted Answer

To find the mass of $813,000,000$ electrons, we need to multiply the mass of one electron ($9.11 \times 10 ^ { - 28 }$ grams) by the number of electrons.
$$mass = (9.11 \times 10 ^ { - 28 }) \times (813,000,000)$$
Using a calculator, we get:
$$mass = 7.40843 \times 10 ^ { - 19 }$$
Rounding to one decimal place gives:
$$mass \approx 7.4 \times 10 ^ { - 19 }$$
Therefore, the answer is choice C.

Question 19

Solve the problem. Express your answer in scientific notation, and round to one decimal place.
-Approximately 7 × 103 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?

Accepted Answer

The total amount earned by all employees is found by multiplying the number of employees by the average salary per employee: $7 \times 10^3 \times 30,000 = 7 \times 3 \times 10^4 = 21 \times 10^4 = 2.1 \times 10^8$.

Question 20

Perform the indicated calculation. Express your answer using scientific notation.
-$$\left( 3 \times 10 ^ { 5 } \right) \left( 7 \times 10 ^ { 8 } \right)$$

Accepted Answer

To multiply numbers in scientific notation, we multiply the coefficients and add the exponents. Therefore, $(3 	imes 10^5)(7 	imes 10^8) = (3 \cdot 7) 	imes 10^{5+8} = 21 	imes 10^{13} = 2.1 	imes 10^{14}$. The correct answer is B.

Quiz 5: Exponents and Polynomials

Convert the given number to scientific notation. -0.000014914

Convert the given number to scientific notation. -1,037,000,000,000,000

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -A computer can do one calculation in 1.4 × 10-7 seconds. How long would it take the computer to do a million (106) calculations?

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -In a state with a population of 7,000,000 people, the average citizen spends $6,000 on housing each year. What is the total spent on housing for the state?

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 9.24 \times 10 ^ { 5 } \right) \div \left( 4.4 \times 10 ^ { - 6 } \right)$

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 6.6 \times 10 ^ { - 3 } \right) \left( 7.4 \times 10 ^ { 8 } \right)$

Perform the indicated calculation. Express your answer using scientific notation. - $( 6,350,000,000 ) \div ( 2,318,000 )$

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 15 \times 10 ^ { - 5 } \right) \div \left( 3 \times 10 ^ { 4 } \right)$

Convert the given number to scientific notation. -0.0000000381018

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 1.9 \times 10 ^ { - 7 } \right) \left( 1.6 \times 10 ^ { - 4 } \right)$

Convert the given number to scientific notation. -0.000000215019

Convert the given number to scientific notation. -1,086,000,000,000,000,000

Convert the given number to scientific notation. -0.000009447

Convert the given number to scientific notation. -83,000,000

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 15.64 \times 10 ^ { 3 } \right) \div \left( 4 \times 10 ^ { - 5 } \right)$

Perform the indicated calculation. Express your answer using scientific notation. - $( 0.0000000064 ) ( 160,000,000,000 )$

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -The speed of light is 1.86 × 105 miles/second. How far can light travel in one year? Round to one decimal place.

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -The mass of an electron is approximately $9.11 \times 10 ^ { - 28 }$ grams. Find the mass of $813,000,000$ electrons.

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -Approximately 7 × 103 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?

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 3 \times 10 ^ { 5 } \right) \left( 7 \times 10 ^ { 8 } \right)$