Question 1

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.
-Last year the total amount spent by Americans on food was about $10 ^ { 11 }$ dollars.

Accepted Answer

The answer of Determine whether the statement makes sense. If...

Question 2

Determine whether the source of error represents random or systematic error.
-You time how long you spend working out each day. Your watch is running slow and loses one minute each hour.
A)Systematic error
B)Random error

Accepted Answer

This is a systematic error because the watch consistently loses one minute each hour, leading to a predictable and repeatable discrepancy in the timing measurements.

Question 3

Write the number in ordinary notation.
-$2.116 \times 10 ^ { - 6 }$
A) $- 2,116,000$
B) $0.00002116$
C) $0.0000002116$
D) $0.000002116$

Accepted Answer

The notation $2.116 \times 10^{-6}$ means the decimal point in 2.116 is moved 6 places to the left, resulting in 0.000002116.

Question 4

Restate the fact as indicated.
-Worldwide there are approximately 132 million births per year. Express this quantity in births per second.
A)4.2 births per second
B)251 births per second
C)63,300 births per second
D)101 births per second

Accepted Answer

To convert the number of births per year to births per second, divide the total number of births per year by the number of seconds in a year (365 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute). This calculation gives approximately 4.2 births per second.

Question 5

True or false?
-Given that Sue's weight increased from 120 lb to 132 lb and that Mark's weight increased from 150
lb to 165 lb, we can say that in absolute terms, Mark's weight increased more, but that in relative
terms, Sue's weight increased more.

Accepted Answer

The answer of True or false?
-Given that Sue's weight increased...

Question 6

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated.
-The weight of the child is 6 kilos while the weight of her father is 97.9 kilos. 97.9 kilos is what percent of 6 kilos?
A)16,317.0
B)6.1
C)1631.7
D)0.6

Accepted Answer

To find what percent 97.9 kilos is of 6 kilos, you divide 97.9 by 6 and then multiply by 100. Doing the math: $ \frac{97.9}{6} \times 100 = 1631.7 $.

Question 7

Round to the indicated place value.
-Round to the nearest ten thousandth: 14.58578
A)14.5858
B)14.5857
C)14.586
D)14.59

Accepted Answer

The fifth digit after the decimal is 8, which rounds the fourth digit up from 7 to 8, making the number 14.5858 when rounded to the nearest ten thousandth.

Question 8

Measurements are made at two different times. Find the absolute change and then find the percentage change. Roundanswers to the nearest tenth if necessary.
-The value of Anna's house increased from $160,000 when she bought it 20 years ago to $1.38 million today. 
A) Absolute change: $\$ - 1,220,000$
Percentage change: 762.5\%

B) Absolute change: $\$ 1,220,000$ 
Percentage change: 76.3\%

C) Absolute change: $\$ 1,220,000$
Percentage change: $762.5 \%$

D) Absolute change: $\$ 1,220,000$ 
Percentage change: $88.4 \%$

Accepted Answer

The absolute change is the difference between the final value and the initial value, which is $1,380,000 - $160,000 = $1,220,000. The percentage change is calculated as (Absolute change / Initial value) * 100 = ($1,220,000 / $160,000) * 100 = 762.5%.

Question 9

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated.
-Chuck has saved $364 at the bank. He wants to save $2300 for a trip to Alaska. What percent of his goal has been reached?
A)15.8%
B)6.3%
C)1.6%
D)63%

Accepted Answer

To find the percentage of the goal reached, divide the amount saved ($364) by the total goal ($2300) and multiply by 100. $ \frac{364}{2300} \times 100 = 15.826... $%, which rounds to 15.8%.

Question 10

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is thanthe second.
-$3 \times 10 ^ { - 8 } , 3 \times 10 ^ { - 32 }$
A) $10 ^ { 1 / 4 }$
B) $10 ^ { 40 }$
C) $10 ^ { - 24 }$
D) $10 ^ { 24 }$

Accepted Answer

To find how many times larger the first number is than the second, divide the first number by the second: $ \frac{3 \times 10^{-8}}{3 \times 10^{-32}} = 10^{(-8) - (-32)} = 10^{24} $.

Question 11

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated.
-Tech Support spent $18,450 this year on utility costs alone. If total sales were $268,200, what percent of total sales was spent on utility costs? Round to the nearest tenth of a percent.
A)0.7%
B)14.5%
C)145.0%
D)6.9%

Accepted Answer

To find the percentage of total sales spent on utility costs, divide the utility costs by the total sales and then multiply by 100. $ \frac{18,450}{268,200} \times 100 = 6.9\% $.

Question 12

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.
-The book contains $10 ^ { 6 }$ letters.

Accepted Answer

A book containing $10^6$ letters is possible, as this equates to 1,000,000 letters, which is a reasonable length for a large book.

Question 13

Write the number in ordinary notation.
-$5.4 \times 10 ^ { 5 }$
A) $5,400,000$
B) 54,000
C) 270
D) 540,000

Accepted Answer

The notation $5.4 \times 10^5$ means that the decimal point in 5.4 is moved 5 places to the right, resulting in 540,000.

Question 14

Solve the problem.
-A store manager paid $192 for an item and set the selling price at $261.12. What was the percent markup?
A)26%
B)35%
C)36%
D)34%

Accepted Answer

The percent markup is calculated as the difference between the selling price and the cost price, divided by the cost price, then multiplied by 100. Here, it is (($261.12 - $192) / $192) * 100 = 36%.

Question 15

Solve the problem.
-The table below shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. Use the table to answer the question.  What percentage of those that tested positive actually have the disease?
A)87.4%
B)1.3%
C)1.1%
D)9.9%

Accepted Answer

The answer of Solve the problem.
-The table below shows the...

Question 16

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits.
-If you buy 228 items which weigh 0.038 lb each, what is the total weight of your purchase?
A)8.664 lb
B)8.7 lb
C)9 lb
D)8.66 lb

Accepted Answer

The total weight is calculated as 228 items * 0.038 lb/item = 8.664 lb. According to significant figures rules, the least number of decimal places in the given data is 3 (in 0.038), so the answer should be rounded to the nearest tenth, making it 8.7 lb.

Question 17

Find the absolute and relative errors.
-The true distance from your home to your office is 33.5 miles but your odometer reads 35.1 miles. 
A) absolute error: $- 1.6$ miles
$\text { relative error: }-4.8 \%$

B) absolute error: $1.6$ miles
relative error: $4.6 \%$

C) absolute error: $1.6$ miles
miles relative error: $0.5 \%$

D) absolute error: $1.6$ 
 relative error: $4.8 \%$

Accepted Answer

The absolute error is the difference between the measured value and the true value, which is $35.1 - 33.5 = 1.6$ miles. The relative error is the absolute error divided by the true value, then multiplied by 100 to get a percentage, which is $\frac{1.6}{33.5} \times 100 \approx 4.7761\%$, rounded to $4.8\%$.

Question 18

True or false?
-In Fremont in 1990, the mayor's approval rating was 80%. In 1998, his approval rating was only
64%.
True or false? in absolute terms his approval rating decreased by 16 percentage points whereas in
relative terms, it decreased by 20%.

Accepted Answer

The absolute decrease is 80% - 64% = 16 percentage points. The relative decrease is (16/80) * 100% = 20%.

Question 19

Solve the problem.
-The table below shows a housing index that can be used to compare housing prices in different cities. $$\begin{array} { l | c } 
\text { CITY } & \text { INDEX } \
\hline \text { Juneau, AK } & 100 \
\text { Palo Alto, CA } & 365 \
\text { Denver, CO } & 87 \
\text { Spokane, WA } & 78 \
\text { Boston, MA } & 182 \
\text { Manhattan, NY } & 495
\end{array}$$ Suppose you see a house valued at $190,000 in Spokane. Find the price of a comparable house in
Manhattan.
A)$1,326,346
B)$1,205,769
C)$29,939
D)$1,085,192

Accepted Answer

The answer of Solve the problem.
-The table below shows a...

Question 20

Solve for the percentage in the problem. Round to the nearest tenth of a percent.
-______ $\text { \% of } 170 \text { cartons is } 10.1 \text { cartons. }$
A)0.1
B)1683.2
C)0.2
D)5.9

Accepted Answer

To find the percentage, use the formula: $\frac{part}{whole} \times 100$. Here, the part is 10.1 cartons, and the whole is 170 cartons. So, $\frac{10.1}{170} \times 100 = 5.941...$, which rounds to 5.9%.

Quiz 3: Numbers in the Real World

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. -Last year the total amount spent by Americans on food was about $10 ^ { 11 }$ dollars.

Determine whether the source of error represents random or systematic error. -You time how long you spend working out each day. Your watch is running slow and loses one minute each hour.

Write the number in ordinary notation. - $2.116 \times 10 ^ { - 6 }$

Restate the fact as indicated. -Worldwide there are approximately 132 million births per year. Express this quantity in births per second.

True or false? -Given that Sue's weight increased from 120 lb to 132 lb and that Mark's weight increased from 150 lb to 165 lb, we can say that in absolute terms, Mark's weight increased more, but that in relative terms, Sue's weight increased more.

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. -The weight of the child is 6 kilos while the weight of her father is 97.9 kilos. 97.9 kilos is what percent of 6 kilos?

Round to the indicated place value. -Round to the nearest ten thousandth: 14.58578

Measurements are made at two different times. Find the absolute change and then find the percentage change. Roundanswers to the nearest tenth if necessary. -The value of Anna's house increased from $160,000 when she bought it 20 years ago to $1.38 million today.

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. -Chuck has saved $364 at the bank. He wants to save $2300 for a trip to Alaska. What percent of his goal has been reached?

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is thanthe second. - $3 \times 10 ^ { - 8 } , 3 \times 10 ^ { - 32 }$

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. -Tech Support spent $18,450 this year on utility costs alone. If total sales were $268,200, what percent of total sales was spent on utility costs? Round to the nearest tenth of a percent.

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. -The book contains $10 ^ { 6 }$ letters.

Write the number in ordinary notation. - $5.4 \times 10 ^ { 5 }$

Solve the problem. -A store manager paid $192 for an item and set the selling price at $261.12. What was the percent markup?

Solve the problem. -The table below shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. Use the table to answer the question. What percentage of those that tested positive actually have the disease?

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits. -If you buy 228 items which weigh 0.038 lb each, what is the total weight of your purchase?

Find the absolute and relative errors. -The true distance from your home to your office is 33.5 miles but your odometer reads 35.1 miles.

True or false? -In Fremont in 1990, the mayor's approval rating was 80%. In 1998, his approval rating was only 64%. True or false? in absolute terms his approval rating decreased by 16 percentage points whereas in relative terms, it decreased by 20%.

Solve for the percentage in the problem. Round to the nearest tenth of a percent. -______ $\text { \% of } 170 \text { cartons is } 10.1 \text { cartons. }$