Question 1

Write as a percent.
-$5.4$

Accepted Answer

A)  $540 \%$ 
B)  $54 \%$ 
C)  $0.0054 \%$ 
D)  $0.54 \%$ 
A)  $540 \%$ 
B)  $54 \%$ 
C)  $0.0054 \%$ 
D)  $0.54 \%$

Question 2

Answer the question.
-Your true weight is $62.66$ kilograms. A scale that gives weights to the nearest quarter kilogram gives your weight as $62 \frac { 3 } { 4 }$ kilograms. A digital scale that gives weights to the nearest $0.1$ kilogram gives your weight as $62.6$ kilograms. Which of these two measurement is more precise? Which is more accurate?

Accepted Answer

A)  The digital scale gives a more precise reading but the first scale gives a more accurate reading. 
B)  The first scale gives a more precise reading and also a more accurate reading. 
C)  The digital scale gives a more precise reading and also a more accurate reading. 
D)  The first scale gives a more precise reading but the digital scale gives a more accurate reading. 
A)  The digital scale gives a more precise reading but the first scale gives a more accurate reading. 
B)  The first scale gives a more precise reading and also a more accurate reading. 
C)  The digital scale gives a more precise reading and also a more accurate reading. 
D)  The first scale gives a more precise reading but the digital scale gives a more accurate reading.

Question 3

Solve the problem.
-The percentage of registered voters who voted in this election was 54%, up 20% from the last election. What was the percentage that voted at the last election?

Accepted Answer

A) 45% 
B) 64.8% 
C) 43.2% 
D) 34% 
A) 45% 
B) 64.8% 
C) 43.2% 
D) 34%

Question 4

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
-The total amount of money spent each year on food by Americans.

Accepted Answer

A) Ten billion dollars 
B) One trillion dollars 
C) Thirty trillion dollars 
D) One hundred billion dollars 
A) Ten billion dollars 
B) One trillion dollars 
C) Thirty trillion dollars 
D) One hundred billion dollars

Question 5

Decide whether the statement is believable, given the precision with which it is stated.
-A business projects next year's profits to be $4,740,000.

Accepted Answer

A) Not believable at that precision 
B) Believable 
A) Not believable at that precision 
B) Believable

Question 6

Write the percentage as a fraction or decimal, as indicated.
-Write as a fraction. $83 \frac { 1 } { 3 } \%$

Accepted Answer

A)  $\frac { 25 } { 3 }$ 
B)  $\frac { 5 } { 12 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  $\frac { 5 } { 6 }$ 
A)  $\frac { 25 } { 3 }$ 
B)  $\frac { 5 } { 12 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  $\frac { 5 } { 6 }$

Question 7

Answer the question.
-Which of the statements below suggests an appropriate level of precision?

Accepted Answer

A) The number of people at the demonstration was 120,000. 
B) The number of people at the demonstration was 122,600. 
C) The number of people at the demonstration was 100,000 [to the nearest one hundred thousand]. 
D) The number of people at the demonstration was 122,615. 
A) The number of people at the demonstration was 120,000. 
B) The number of people at the demonstration was 122,600. 
C) The number of people at the demonstration was 100,000 [to the nearest one hundred thousand]. 
D) The number of people at the demonstration was 122,615.

Question 8

Round to the indicated place value.
-Round to the nearest hundredth: $20.17458$

Accepted Answer

A)  $20.1746$ 
B)  $20.175$ 
C)  $20.17$ 
D)  $20.18$ 
A)  $20.1746$ 
B)  $20.175$ 
C)  $20.17$ 
D)  $20.18$

Question 9

Find the absolute and relative errors.
-The length of the room is 12 feet but you measure it to be 12 feet and 5 inches.

Accepted Answer

A) absolute error: -5 inches 
B) absolute error: 5 inches relative error: -3.5% relative error: 3.4% 
C) absolute error: 5 inches 
D) absolute error: 5 inches relative error: 3.5% relative error: 4.2% 
A) absolute error: -5 inches 
B) absolute error: 5 inches relative error: -3.5% relative error: 3.4% 
C) absolute error: 5 inches 
D) absolute error: 5 inches relative error: 3.5% relative error: 4.2%

Question 10

State the number of significant digits and the implied precision of the given number.
-$6.500 \times 10 ^ { 7 }$

Accepted Answer

A)  4 significant digits, precise to the nearest thousandth 
B)  8 significant digits, precise to the nearest unit 
C)  2 significant digits, precise to the nearest 10,000 
D)  4 significant digits, precise to the nearest 10,000 
A)  4 significant digits, precise to the nearest thousandth 
B)  8 significant digits, precise to the nearest unit 
C)  2 significant digits, precise to the nearest 10,000 
D)  4 significant digits, precise to the nearest 10,000

Question 11

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 unemployment rate in Midtown a decade ago was 20%. This year it was 36%.

Accepted Answer

A)  Absolute change: 16 percentage points
 Percentage change: $44.4 \%$ 
B)  Absolute change: 80 percentage points 
Percentage change: 16\% 
C)  Absolute change: $- 16$ percentage points
Percentage change: $44.4 \%$ 
D)  Absolute change: 16 percentage points 
Percentage change: $80 \%$ 
A)  Absolute change: 16 percentage points
 Percentage change: $44.4 \%$ 
B)  Absolute change: 80 percentage points 
Percentage change: 16\% 
C)  Absolute change: $- 16$ percentage points
Percentage change: $44.4 \%$ 
D)  Absolute change: 16 percentage points 
Percentage change: $80 \%$

Question 12

True or false?
-If I earn 60% more than you, then you must earn 37.5% less than me.

Accepted Answer

A) True 
 B)False

Question 13

Solve the problem.
-Suppose the current cost of gasoline is $\$ 3.22$ per gallon. Find the current price index using the 1975 price as the reference value. In 1975 , the cost of gasoline was $56.7$ cents per gallon.

Accepted Answer

A)  $265.3$ 
B)  $567.9$ 
C)  $17.6$ 
D)  $5.7$ 
A)  $265.3$ 
B)  $567.9$ 
C)  $17.6$ 
D)  $5.7$

Question 14

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

Accepted Answer

A)  $10 ^ { 1 / 4 }$ 
B)  $10 ^ { 40 }$ 
C)  $10 ^ { - 24 }$ 
D)  $10 ^ { 24 }$ 
A)  $10 ^ { 1 / 4 }$ 
B)  $10 ^ { 40 }$ 
C)  $10 ^ { - 24 }$ 
D)  $10 ^ { 24 }$

Question 15

Use the Consumer Price Index below to answer the question. $$\begin{array}{l}
\text { Average Annual Consumer Price Index (1982-1984 = 100) }\
\begin{array} { c | c | c | c | c | c } 
\text { Year } & \text { CPI } & \text { Year } & \text { CPI } & \text { Year } & \text { CPI } \
\hline 1986 & 109.6 & 1995 & 152.4 & 2004 & 188.9 \
1987 & 113.6 & 1996 & 156.9 & 2005 & 195.3 \
1988 & 118.3 & 1997 & 160.5 & 2006 & 201.6 \
1989 & 124.0 & 1998 & 163.0 & 2007 & 207.3 \
1990 & 130.7 & 1999 & 166.6 & 2008 & 215.3 \
1991 & 136.2 & 2000 & 172.2 & 2009 & 214.5 \
1992 & 140.3 & 2001 & 177.1 & 2010 & 218.1 \
1993 & 144.5 & 2002 & 179.9 & 2011 & 224.9 \
1994 & 148.2 & 2003 & 184.0 & 2012 & 229.6
\end{array}
\end{array}$$
-Between 1990 and 2000, a college raised its annual tuition fees from $4690 to $6630. Find
the relative change in the fees over that period and compare it to the overall rate of
inflation as measured by the CPI. Were the tuition increases in line with inflation?

Accepted Answer

Relative change in cost @#LAT-DLM&
Overa

Question 16

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
-The weight of a grain of rice.

Accepted Answer

A) 0.0006 ounces 
B) 0.000001 ounces 
C) 0.006 ounces 
D) 0.01 ounces 
A) 0.0006 ounces 
B) 0.000001 ounces 
C) 0.006 ounces 
D) 0.01 ounces

Question 17

Answer the question.
-Between 1990 and 2000, the population of Emeryville grew from 20,000 to 25,000 while the population of Sun City grew from 100,000 to 110,000. Which of the statements below is correct?

Accepted Answer

A) Emeryville had greater absolute growth in population, and also greater relative growth. 
B) Emeryville had greater absolute growth in population, but Sun City had greater relative growth. 
C) Sun City had greater absolute growth in population, and also greater relative growth. 
D) Sun City had greater absolute growth in population, but Emeryville had greater relative growth. 
A) Emeryville had greater absolute growth in population, and also greater relative growth. 
B) Emeryville had greater absolute growth in population, but Sun City had greater relative growth. 
C) Sun City had greater absolute growth in population, and also greater relative growth. 
D) Sun City had greater absolute growth in population, but Emeryville had greater relative growth.

Question 18

Answer the question.
-A researcher looks at the percentage of people having high blood pressure amongst those who exercise regularly and amongst those who do not exercise regularly.
She selects 300 people under 40, of whom 100 exercise regularly and 200 do not. Among those who
Exercise regularly the rate of high blood pressure is 10% and among those who do not exercise
Regularly it is 15%.
She then selects 300 people over 40, of whom 200 exercise regularly and 100 do not. Among those
Who exercise regularly the rate of high blood pressure is 30% and among those who do not exercise
Regularly it is 35%.
However when she combines both age groups she finds that among those who exercise regularly
The rate of high blood pressure is 23.3% and among those who do not exercise regularly it is 21.7%.
Explain how the apparent inconsistency in these results came about.

Accepted Answer

A) Mistakes must have been made in measuring blood pressures. 
B) Those that do not exercise regularly must be receiving some other treatment to lower their blood pressure. 
C) The people in the "regular exercise" group probably started exercising because they have high blood pressure. 
D) The group that exercises regularly contains a greater proportion of older people than the group that does not exercise regularly. So when the age groups are combined, the "regular
Exercise" group has a higher rate of high blood pressure. 
A) Mistakes must have been made in measuring blood pressures. 
B) Those that do not exercise regularly must be receiving some other treatment to lower their blood pressure. 
C) The people in the "regular exercise" group probably started exercising because they have high blood pressure. 
D) The group that exercises regularly contains a greater proportion of older people than the group that does not exercise regularly. So when the age groups are combined, the "regular
Exercise" group has a higher rate of high blood pressure.

Question 19

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is thanthe second.
-$1.2 \times 10 ^ { - 5 } , 4.8 \times 10 ^ { - 15 }$

Accepted Answer

A)  $2.5 \times 10 ^ { 1 / 3 }$ 
B)  $2.5 \times 10 ^ { 10 }$ 
C)  $2.5 \times 10 ^ { 20 }$ 
D)  $2.5 \times 10 ^ { 9 }$ 
A)  $2.5 \times 10 ^ { 1 / 3 }$ 
B)  $2.5 \times 10 ^ { 10 }$ 
C)  $2.5 \times 10 ^ { 20 }$ 
D)  $2.5 \times 10 ^ { 9 }$

Question 20

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 don't have the disease tested negative?

Accepted Answer

A) 98.6% 
B) 90.1% 
C) 99.8% 
D) 88.9% 
A) 98.6% 
B) 90.1% 
C) 99.8% 
D) 88.9%

Write as a percent. - $5.4$

Solve the problem. -The percentage of registered voters who voted in this election was 54%, up 20% from the last election. What was the percentage that voted at the last election?

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. -The total amount of money spent each year on food by Americans.

Decide whether the statement is believable, given the precision with which it is stated. -A business projects next year's profits to be $4,740,000.

Write the percentage as a fraction or decimal, as indicated. -Write as a fraction. $83 \frac { 1 } { 3 } \%$

Answer the question. -Which of the statements below suggests an appropriate level of precision?

Round to the indicated place value. -Round to the nearest hundredth: $20.17458$

Find the absolute and relative errors. -The length of the room is 12 feet but you measure it to be 12 feet and 5 inches.

State the number of significant digits and the implied precision of the given number. - $6.500 \times 10 ^ { 7 }$

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 unemployment rate in Midtown a decade ago was 20%. This year it was 36%.

True or false? -If I earn 60% more than you, then you must earn 37.5% less than me.

Solve the problem. -Suppose the current cost of gasoline is $\$ 3.22$ per gallon. Find the current price index using the 1975 price as the reference value. In 1975 , the cost of gasoline was $56.7$ cents per gallon.

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

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. -The weight of a grain of rice.

Answer the question. -Between 1990 and 2000, the population of Emeryville grew from 20,000 to 25,000 while the population of Sun City grew from 100,000 to 110,000. Which of the statements below is correct?

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is thanthe second. - $1.2 \times 10 ^ { - 5 } , 4.8 \times 10 ^ { - 15 }$

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 don't have the disease tested negative?

Thinking Critically

Approaches to Problem Solving

Managing Money

Statistical Reasoning

Putting Statistics to Work

Probability: Living With the Odds

Exponential Astonishment

Modeling Our World

Modeling With Geometry

Mathematics and the Arts

Filters

Exam 3: Numbers in the Real World

Write as a percent. - 5.45.45.4