Question 1

Write the number in scientific notation.
-$0.00003311$

Accepted Answer

To write this number in scientific notation, we need to move the decimal point 5 places to the right (since the number is less than 1) and add a negative exponent. This gives us $3.311 \times 10^{-5}$.

Question 2

Write the number in scientific notation.
-$$630,000$$

Accepted Answer

To write 630,000 in scientific notation, you move the decimal point 5 places to the left, which gives $6.3 \times 10^5$.

Question 3

Simplify.
-$\left( \frac { b ^ { 2 } } { 2 } \right) ^ { - 5 }$

Accepted Answer

When simplifying $\left( \frac { b ^ { 2 } } { 2 } \right) ^ { - 5 }$, you apply the negative exponent rule, which flips the fraction and raises both the numerator and denominator to the power of 5. This results in $\frac { 32 } { b ^ { 10 } }$.

Question 4

Write the number in scientific notation.
-$339.749$

Accepted Answer

To convert to scientific notation, move the decimal point to the left until only one non-zero digit is to the left of the decimal, resulting in $3.39749	imes 10^2.$

Question 5

If the number in the statement is written in scientific notation, write it without exponents. If it is written without
exponents, write it in scientific notation.
-The earth is approximately $92,900,000$ miles from the sun.

Accepted Answer

The number 92,900,000 written in scientific notation is $9.29 \times 10^7$, moving the decimal point 7 places to the left.

Question 6

Write the number in scientific notation.
-$0.0000000120014$

Accepted Answer

To convert the number to scientific notation, we need to move the decimal point 10 places to the right because there are 10 zeros between the decimal point and the first non-zero digit. This gives us 1.20014. However, since we moved the decimal point to the right, we need to multiply by a negative power of 10 to compensate, which gives us the final answer of $1.20014 \times 10^{-8}$.

Question 7

If the number in the statement is written in scientific notation, write it without exponents. If it is written without
exponents, write it in scientific notation.
-The population of a small country is $2,038,000$.

Accepted Answer

The number in the statement is already written without exponents, so we need to convert it to scientific notation. Moving the decimal point to the left until we have a number between 1 and 10, we get:

2.038000

Now count the number of places you moved the decimal point to get this number. In this case, we moved it 6 places to the left. Therefore, the number in scientific notation is:

2.038 x 10^6

Question 8

Write the number in scientific notation.
-$0.000000479012$

Accepted Answer

The number can be written in scientific notation by shifting the decimal point 7 places to the right and making the coefficient between 1 and 10. This gives us $4.79012$ as the coefficient and $10^{-7}$ as the power of 10. Therefore, the correct choice is D.

Question 9

Simplify.
-$\left( \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 8 } } \right) ^ { 4 }$

Accepted Answer

When raising an exponent to another exponent, we multiply the exponents. Therefore, we have: 
$$\left( \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 8 } } \right) ^ { 4 } = \frac{ x ^ { 3\cdot 4 } } { y ^ { 3\cdot 4} z ^ { 8\cdot 4 } }=\frac { x ^ { 12 } } { y ^ { 12 } z ^ { 32 } }$$

Question 10

Write the number in scientific notation.
-597.08

Accepted Answer

To write a number in scientific notation, we need to 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 two places to the right to get 5.9708. This is equivalent to multiplying by 100, or 10². Therefore, the scientific notation is 5.9708 × 10².

Question 11

Simplify.
-$\left( \frac { x y ^ { 2 } } { w ^ { 6 } z } \right) ^ { - 4 }$

Accepted Answer

To simplify $\left( \frac { x y ^ { 2 } } { w ^ { 6 } z } \right) ^ { - 4 }$, you invert the fraction and raise each variable to the power of -4, resulting in $\frac { w ^ { 24 } z ^ { 4 } } { x ^ { 4 } y ^ { 8 } }$.

Question 12

If the number in the statement is written in scientific notation, write it without exponents. If it is written without
exponents, write it in scientific notation.
-A company produces 677,000 small appliances in one year.

Accepted Answer

The number 677,000 can be written in scientific notation as 6.77 x 10^5. Therefore, choice C is the correct answer.

Question 13

If the number in the statement is written in scientific notation, write it without exponents. If it is written without
exponents, write it in scientific notation.
-It has been estimated that the average American watches 58,240 hours of television in a lifetime.

Accepted Answer

The correct scientific notation for 58,240 is $5.824 \times 10^{4}$ hours, as it moves the decimal point 4 places to the left to express the number.

Question 14

Write the number in scientific notation.
-$5,800,000$

Accepted Answer

To write in 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 would move the decimal point six places to the left to get 5.8. Since we moved the decimal point to the left, we need to multiply by a power of 10. The number of places we moved the decimal point determines the exponent on 10, which is 6 in this case. Therefore, the answer is 5.8 x 10^6.

Question 15

Write the number in scientific notation.
-$0.0000019214$

Accepted Answer

To convert to scientific notation, we move the decimal point 6 places to the left because the number is less than 1. This gives us $1.9214 	imes 10^{-6}$.

Question 16

If the number in the statement is written in scientific notation, write it without exponents. If it is written without
exponents, write it in scientific notation.
-The life span of the average male human being is approximately $37,843,200$ minutes.

Accepted Answer

The correct scientific notation for $37,843,200$ is $3.78432 \times 10^{7}$ minutes, as it moves the decimal place 7 positions to the left.

Question 17

Write the number in scientific notation.
-$0.000973$

Accepted Answer

In scientific notation, the number must be between 1 and 10. To move the decimal point to the right so that 0.000973 becomes a number between 1 and 10, we must move it 4 places to the right. This gives us 9.73. However, we moved the decimal point 4 places to the right, so our exponent is -4. Therefore, the number in scientific notation is 9.73 × 10^-4. This corresponds to choice C.

Question 18

If the number in the statement is written in scientific notation, write it without exponents. If it is written without
exponents, write it in scientific notation.
-The speed of light is $1.86 \times 10 ^ { 5 }$ miles per hour.

Accepted Answer

Writing the number in scientific notation means moving the decimal point to create a number between 1 and 10, and multiplying by a power of 10. In this case, moving the decimal point to the left gives 1.86, which is between 1 and 10. Multiplying by 10^5 gives 186,000, which is the answer in choice A.

Question 19

If the number in the statement is written in scientific notation, write it without exponents. If it is written without
exponents, write it in scientific notation.
-A computer can do one calculation in $1.4 \times 10 ^ { - 7 }$ seconds.

Accepted Answer

The scientific notation $1.4 \times 10^{-7}$ seconds is equivalent to $0.00000014$ seconds when written without exponents.

Question 20

Write the number in scientific notation.
-878,835

Accepted Answer

To convert to scientific notation, we move the decimal point 5 places to the left and add a power of 10 to compensate. This gives us $8.78835 \times 10 ^ {5}$. Therefore, the correct answer is choice D.

Quiz 4: Polynomials: Operations

Write the number in scientific notation. - $0.00003311$

Write the number in scientific notation. - $630,000$

Simplify. - $\left( \frac { b ^ { 2 } } { 2 } \right) ^ { - 5 }$

Write the number in scientific notation. - $339.749$

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The earth is approximately $92,900,000$ miles from the sun.

Write the number in scientific notation. - $0.0000000120014$

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The population of a small country is $2,038,000$ .

Write the number in scientific notation. - $0.000000479012$

Simplify. - $\left( \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 8 } } \right) ^ { 4 }$

Write the number in scientific notation. -597.08

Simplify. - $\left( \frac { x y ^ { 2 } } { w ^ { 6 } z } \right) ^ { - 4 }$

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -A company produces 677,000 small appliances in one year.

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -It has been estimated that the average American watches 58,240 hours of television in a lifetime.

Write the number in scientific notation. - $5,800,000$

Write the number in scientific notation. - $0.0000019214$

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The life span of the average male human being is approximately $37,843,200$ minutes.

Write the number in scientific notation. - $0.000973$

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The speed of light is $1.86 \times 10 ^ { 5 }$ miles per hour.

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -A computer can do one calculation in $1.4 \times 10 ^ { - 7 }$ seconds.

Write the number in scientific notation. -878,835

Quiz 4: Polynomials: Operations

Write the number in scientific notation. - 0.000033110.000033110.00003311

Write the number in scientific notation. - 630,000630,000630,000

Simplify. - (b22) −5\left( \frac { b ^ { 2 } } { 2 } \right) ^ { - 5 }(2b2​) −5

Write the number in scientific notation. - 339.749339.749339.749

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The earth is approximately 92,900,00092,900,00092,900,000 miles from the sun.

Write the number in scientific notation. - 0.00000001200140.00000001200140.0000000120014

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The population of a small country is 2,038,0002,038,0002,038,000 .

Write the number in scientific notation. - 0.0000004790120.0000004790120.000000479012

Simplify. - (x3y3z8) 4\left( \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 8 } } \right) ^ { 4 }(y3z8x3​) 4