Question 1

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. 
A) $37.8432 \times 10 ^ { 6 }$ minutes
B) $3.78432 \times 10 ^ { 6 }$ minutes
C) $3.78432 \times 10 ^ { 7 }$ minutes
D) $3.78432 \times 10 ^ { 5 }$ minutes

Accepted Answer

To convert the number 37,843,200 to scientific notation, we move the decimal point 7 places to the left, which gives us $3.78432 \times 10^{7}$ minutes.

Question 2

Write the number in scientific notation.
-770,000 
A) $7.7 \times 10 ^ { 5 }$
B) $7.7 \times 10 ^ { 4 }$
C) $7.7 \times 10 ^ { - 4 }$
D) $7.7 \times 10 ^ { - 5 }$

Accepted Answer

To write 770,000 in scientific notation, you move the decimal point 5 places to the left, which gives $7.7 \times 10^5$.

Question 3

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.
A) $5.824 \times 10 ^ { 4 }$ hours
B) $5.824 \times 10 ^ { 3 }$ hours
C) $58.24 \times 10 ^ { 3 }$ hours
D) $5.824 \times 10 ^ { 5 }$ hours

Accepted Answer

The correct scientific notation for 58,240 is $5.824 \times 10^{4}$ hours, because you move the decimal point 4 places to the left to get from 58,240 to 5.824.

Question 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.
-The population of a small country is 6,344,000 . 
A) $6.344 \times 10 ^ { 5 }$
B) $6.344 \times 10 ^ { - 5 }$
C) $6.344 \times 10 ^ { 4 }$
D) $6.344 \times 10 ^ { 6 }$

Accepted Answer

The population of 6,344,000 written in scientific notation is $6.344 \times 10^6$, as the decimal point is moved 6 places to the left to place it after the first non-zero digit.

Question 5

Write the number in scientific notation.
-453.29 
A) $4.5329 \times 10 ^ { - 2 }$
B) $4.5329 \times 10 ^ { - 3 }$
C) $4.5329 \times 10 ^ { 2 }$
D) $4.5329 \times 10 ^ { 3 }$

Accepted Answer

To convert 453.29 to scientific notation, we move the decimal point 2 places to the left, making it $4.5329$. Since we moved the decimal to the left, the exponent is positive, resulting in $4.5329 \times 10^{2}$.

Question 6

Write the number in scientific notation.
-0.0000000862016 
A) $8.62016 \times 10 ^ { - 8 }$
B) $8.62016 \times 10 ^ { - 7 }$
C) $8.62016 \times 10 ^ { 8 }$
D) $8.62016 \times 10 ^ { - 9 }$

Accepted Answer

To convert a number to scientific notation, you move the decimal point to the right of its first non-zero digit. For 0.0000000862016, you move the decimal 8 places to the right, resulting in $8.62016 \times 10^{-8}$.

Question 7

Write the number in scientific notation.
-0.00000070109 
A) $7.0109 \times 10 ^ { - 7 }$
B) $7.0109 \times 10 ^ { - 6 }$
C) $7.0109 \times 10 ^ { 6 }$
D) $7.0109 \times 10 ^ { 7 }$

Accepted Answer

To convert 0.00000070109 to scientific notation, we move the decimal point 7 places to the right, making it $7.0109 \times 10^{-7}$.

Question 8

Simplify.
-$\left( \frac { b ^ { 6 } } { 5 } \right) ^ { - 2 }$
A) $\frac { b ^ { - 12 } } { 5 }$
B) $\frac { 25 } { b ^ { 12 } }$
C) $\frac { b ^ { 12 } } { 5 ^ { 2 } }$
D) $\frac { b ^ { - 8 } } { 5 ^ { - 2 } }$

Accepted Answer

When simplifying $\left( \frac { b ^ { 6 } } { 5 } \right) ^ { - 2 }$, you apply the negative exponent rule, which inverts the fraction and squares both the numerator and the denominator. This results in $\frac { 25 } { b ^ { 12 } }$, because $5^{-2} = 25$ and $b^{6 \times -2} = b^{-12}$, which then inverts to $b^{12}$ in the denominator.

Question 9

Write the number in scientific notation.
-0.000030116 
A) $3.0116 \times 10 ^ { 4 }$
B) $3.0116 \times 10 ^ { - 4 }$
C) $3.0116 \times 10 ^ { - 5 }$
D) $3.0116 \times 10 ^ { 5 }$

Accepted Answer

To convert 0.000030116 to scientific notation, we move the decimal point 5 places to the right, making it $3.0116 \times 10^{-5}$.

Question 10

Simplify.
-$\left( \frac { x y ^ { 4 } } { w ^ { 6 } z } \right) ^ { - 6 }$
A) $\frac { x y ^ { - 24 } } { w ^ { - 36 } z }$
B) $\frac { x ^ { - 6 } y ^ { - 2 } } { w ^ { 0 } z ^ { - 6 } }$
C) $\frac { x ^ { 6 } y ^ { - 24 } } { w ^ { - 36 } z ^ { 6 } }$
D) $\frac { w ^ { 36 } z ^ { 6 } } { x ^ { 6 } y ^ { 24 } }$

Accepted Answer

When you raise a fraction to a negative exponent, you invert the fraction and change the sign of the exponent. Here, each factor in the fraction gets raised to the power of -6, flipping the base's exponent sign.

Question 11

Simplify.
-$\left( \frac { x ^ { 5 } } { y ^ { 5 } z ^ { 6 } } \right) ^ { 3 }$
A) $\frac { x ^ { 15 } } { y ^ { 5 } z ^ { 18 } }$
B) $\frac { x ^ { 15 } } { y ^ { 15 } z ^ { 18 } }$
C) $\frac { x ^ { 8 } } { y ^ { 9 } z ^ { 9 } }$
D) $\frac { x ^ { 9 } } { y ^ { 15 } z ^ { 18 } }$

Accepted Answer

When raising a power to a power, you multiply the exponents. Thus, $x^5$ raised to the 3rd power becomes $x^{5*3} = x^{15}$, $y^5$ raised to the 3rd power becomes $y^{5*3} = y^{15}$, and $z^6$ raised to the 3rd power becomes $z^{6*3} = z^{18}$, resulting in $\frac{x^{15}}{y^{15}z^{18}}$.

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.
-The earth is approximately 92,900,000 miles from the sun. 
A) $9.29 \times 10 ^ { 8 }$
B) $9.29 \times 10 ^ { 6 }$
C) $9.29 \times 10 ^ { - 7 }$
D) $9.29 \times 10 ^ { 7 }$

Accepted Answer

To convert 92,900,000 to scientific notation, we move the decimal point 7 places to the left, which gives us $9.29 \times 10^7$.

Question 13

Write the number in scientific notation.
-0.000281 
A) $2.81 \times 10 ^ { 4 }$
B) $2.81 \times 10 ^ { - 5 }$
C) $2.81 \times 10 ^ { - 4 }$
D) $2.81 \times 10 ^ { - 3 }$

Accepted Answer

The number 0.000281 can be written as $2.81 \times 10^{-4}$ in scientific notation, as you move the decimal point 4 places to the right to get 2.81.

Question 14

Write the number in scientific notation.
-558,406 
A) $5.58406 \times 10 ^ { 5 }$
B) $5.58406 \times 101$
C) $5.58406 \times 10 ^ { - 5 }$
D) $5.58406 \times 10 ^ { 6 }$

Accepted Answer

To write 558,406 in scientific notation, you move the decimal point 5 places to the left, which gives $5.58406 \times 10^5$.

Question 15

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.
A) $1,860,000$
B) $0.0000186$
C) $18,600,000$
D) 186,000

Accepted Answer

The scientific notation $1.86 \times 10^5$ is equivalent to moving the decimal point 5 places to the right, resulting in 186,000.

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.
-A company produces 916,000 small appliances in one year. 
A) $9.16 \times 10 ^ { 5 }$
B) $9.16 \times 10 ^ { - 5 }$
C) $9.16 \times 10 ^ { 6 }$
D) $91.6 \times 10 ^ { 4 }$

Accepted Answer

916,000 in scientific notation is $9.16 \times 10^5$, as the decimal is moved 5 places to the left.

Question 17

Write the number in scientific notation.
-89,000,000
A)8.9 × 107
B)8.9 × 10-7
C)8.9 × 108
D)8.9 × 10-8

Accepted Answer

To convert 89,000,000 into scientific notation, you move the decimal point 7 places to the left, which gives you 8.9 × 10^7.

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.
-A computer can do one calculation in $1.4 \times 10 ^ { - 7 }$ seconds.
A) $14,000,000$
B) $0.00000014$
C) $0.000000014$
D) $0.000014$

Accepted Answer

$1.4 \times 10^{-7}$ seconds written without exponents is $0.00000014$.

Question 19

Write the number in scientific notation.
-0.000007064 
A) $7.064 \times 10 ^ { - 5 }$
B) $7.064 \times 10 ^ { - 7 }$
C) $7.064 \times 10 ^ { - 6 }$
D) $7.064 \times 10 ^ { 6 }$

Accepted Answer

The number 0.000007064 can be written in scientific notation as $7.064 \times 10^{-6}$ because the decimal point is moved 6 places to the right to get the number 7.064.

Question 20

Write the number in scientific notation.
-377.9 
A) $3.779 \times 10 ^ { - 3 }$
B) $3.779 \times 10 ^ { 2 }$
C) $3.779 \times 10 ^ { - 2 }$
D) $3.779 \times 10 ^ { 3 }$

Accepted Answer

To convert 377.9 to scientific notation, we move the decimal point two places to the left, which gives us $3.779$. To compensate for this shift, we multiply by $10^2$, resulting in $3.779 \times 10^2$.

Quiz 4: Polynomials: Operations

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. -770,000

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.

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 6,344,000 .

Write the number in scientific notation. -453.29

Write the number in scientific notation. -0.0000000862016

Write the number in scientific notation. -0.00000070109

Simplify. - $\left( \frac { b ^ { 6 } } { 5 } \right) ^ { - 2 }$

Write the number in scientific notation. -0.000030116

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

Simplify. - $\left( \frac { x ^ { 5 } } { y ^ { 5 } z ^ { 6 } } \right) ^ { 3 }$

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. -0.000281

Write the number in scientific notation. -558,406

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 company produces 916,000 small appliances in one year.

Write the number in scientific notation. -89,000,000

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. -0.000007064

Write the number in scientific notation. -377.9