Question 1

Use scientific notation to perform the following operations. Leave your answer in scientific notation.
-$\left( 8 \times 10 ^ { 8 } \right) - \left( 5 \times 10 ^ { 7 } \right)$

Accepted Answer

To subtract these numbers, first express them with the same exponent: $8 \times 10^8 = 80 \times 10^7$. Then, $80 \times 10^7 - 5 \times 10^7 = 75 \times 10^7$, which simplifies to $7.5 \times 10^8$.

Question 2

Write the number in scientific notation.
-110,000

Accepted Answer

To convert 110,000 to scientific notation, you move the decimal point 5 places to the left, which gives $1.1 \times 10^5$.

Question 3

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits.
-Subtract the weight 3.2 lb from 279 lb.

Accepted Answer

The correct answer is 276 lb because when subtracting, the answer should have the same decimal places as the number with the least decimal places in the question. Since 279 lb has no decimal places, the answer should be rounded to no decimal places as well.

Question 4

Solve the problem.
-The table below shows a housing index that can be used to compare housing prices in different cities. $$\begin{array} { l | l } 
\text { CITY } & \text { INDEX } \
\hline \text { Juneau, AK } & 100 \
\text { Palo Alto, CA } & 365 \
\text { Denver, CO } & 87 \
\text { Spokane, WA } & 78 \
\text { Boston, MA } & 182 \
\text { Manhattan, NY } & 495
\end{array}$$ Suppose you see a house valued at $710,000 in Palo Alto. Find the price of a comparable house in
Boston.

Accepted Answer

To find the price of a comparable house in Boston, use the ratio of the indices: (182/365) * $710,000 = $354,027.

Question 5

Restate the fact as indicated.
-The population of the United States in 2000 was roughly 280 million. Express this as the number of people per square mile. The land area of the United States is roughly 3,536,000 square miles.

Accepted Answer

To find the number of people per square mile, divide the population by the land area: 280,000,000 people / 3,536,000 square miles = approximately 79 people per square mile.

Question 6

Solve for the percentage in the problem. Round to the nearest tenth of a percent.
-3.5 cases is % of 19.6 cases.

Accepted Answer

To find what percentage 3.5 is of 19.6, use the formula: (part/whole) * 100. So, (3.5/19.6) * 100 = 17.857... which rounds to 17.9%.

Question 7

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible,it does not make sense.
-It would take me about  $1 \times 10 ^ { 6 }$seconds to walk across the United States (from New York to California).

Accepted Answer

Walking across the United States is a long journey, and $1 \times 10^6$ seconds is approximately 11.57 days, which is a reasonable estimate for such a trek if walking continuously without breaks.

Question 8

Write the percentage as a fraction or decimal, as indicated.
-Write as a decimal. 390%

Accepted Answer

To convert a percentage to a decimal, divide by 100. Thus, 390% as a decimal is 390/100 = 3.9.

Question 9

Solve for the percentage in the problem. Round to the nearest tenth of a percent.
-$922.33 is % of $65.91.

Accepted Answer

To find what percentage $922.33 is of $65.91, you use the formula: (Part/Whole) * 100 = Percentage. So, ($922.33/$65.91) * 100 = 1399.4%.

Question 10

Use scientific notation to perform the following operations. Leave your answer in scientific notation.
-$\left( 3.3 \times 10 ^ { 2 } \right) + \left( 2.4 \times 10 ^ { 1 } \right)$

Accepted Answer

To add these numbers, first convert $2.4 \times 10^1$ to the same power of ten as $3.3 \times 10^2$. $2.4 \times 10^1 = 24 = 0.24 \times 10^2$. Then, $3.3 \times 10^2 + 0.24 \times 10^2 = 3.54 \times 10^2$.

Quiz 3: Numbers in the Real World

Use scientific notation to perform the following operations. Leave your answer in scientific notation. - $\left( 8 \times 10 ^ { 8 } \right) - \left( 5 \times 10 ^ { 7 } \right)$

Write the number in scientific notation. -110,000

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits. -Subtract the weight 3.2 lb from 279 lb.

Restate the fact as indicated. -The population of the United States in 2000 was roughly 280 million. Express this as the number of people per square mile. The land area of the United States is roughly 3,536,000 square miles.

Solve for the percentage in the problem. Round to the nearest tenth of a percent. -3.5 cases is % of 19.6 cases.

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible,it does not make sense. -It would take me about $1 \times 10 ^ { 6 }$ seconds to walk across the United States (from New York to California).

Write the percentage as a fraction or decimal, as indicated. -Write as a decimal. 390%

Solve for the percentage in the problem. Round to the nearest tenth of a percent. -$922.33 is % of $65.91.

Use scientific notation to perform the following operations. Leave your answer in scientific notation. - $\left( 3.3 \times 10 ^ { 2 } \right) + \left( 2.4 \times 10 ^ { 1 } \right)$