Question 1

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

Accepted Answer

A) 7.1 
B) 1399.4 
C) 13,994.0 
D) 0.7 
A) 7.1 
B) 1399.4 
C) 13,994.0 
D) 0.7

Question 2

Measurements are made at two different times. Find the absolute change and then find the percentage change. Roundanswers to the nearest tenth if necessary.
-In the last election, in a certain city the percentage of eligible voters who voted in the local election was 63.7%. This year, the percentage fell to 52.9%.

Accepted Answer

A)  Absolute change: $10.8$ percentage points
 Percentage change: $- 17 \%$ 
B)  Absolute change: $10.8$ percentage points
Percentage change: $20.4 \%$ 
C)  Absolute change: $- 10.8$ percentage points
Percentage change: $- 20.4 \%$ 
D)  Absolute change: $- 10.8$ percentage points
Percentage change: $- 17 \%$ 
A)  Absolute change: $10.8$ percentage points
 Percentage change: $- 17 \%$ 
B)  Absolute change: $10.8$ percentage points
Percentage change: $20.4 \%$ 
C)  Absolute change: $- 10.8$ percentage points
Percentage change: $- 20.4 \%$ 
D)  Absolute change: $- 10.8$ percentage points
Percentage change: $- 17 \%$

Question 3

Round to the indicated place value.
-Round to the nearest thousandth: 4.4136

Accepted Answer

A) 4.41 
B) 4.415 
C) 4.414 
D) 4.413 
A) 4.41 
B) 4.415 
C) 4.414 
D) 4.413

Question 4

Measurements are made at two different times. Find the absolute change and then find the percentage change. Roundanswers to the nearest tenth if necessary.
-Last year the Mayor of the town of Little Heath had an approval rating of 71%. This year his approval rating had fallen to 21%.

Accepted Answer

A)  Absolute change: 50 percentage points 
B)  Absolute change: $- 50$ percentage points Percentage change: $238.1 \%$ Percentage change: $- 70.4 \%$ 
C)  Absolute change: $- 50$ percentage points 
D)  Absolute change: $- 50$ percentage points Percentage change: $- 238.1 \%$ Percentage change: $- 7 \%$ 
A)  Absolute change: 50 percentage points 
B)  Absolute change: $- 50$ percentage points Percentage change: $238.1 \%$ Percentage change: $- 70.4 \%$ 
C)  Absolute change: $- 50$ percentage points 
D)  Absolute change: $- 50$ percentage points Percentage change: $- 238.1 \%$ Percentage change: $- 7 \%$

Question 5

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
-The average weight of 100 college-age women, found by asking them their weight during
interviews conducted at their college.

Accepted Answer

Answers may vary. Possible answer
@#LAT-DLM&
women

Question 6

Find the absolute and relative errors.
-Your weight is 127 pounds but the scale indicates that it is 121 pounds.

Accepted Answer

A)  absolute error: -6 pounds
relative error: $- 5 \%$ 
B)  absolute error: 6 pounds 
relative error: $4.7 \%$ 
C)  absolute error: $- 6$ pounds
relative error: $- 4.7 \%$ 
D)  absolute error: $- 6$ pounds 
 relative error: $- 60 \%$ 
A)  absolute error: -6 pounds
relative error: $- 5 \%$ 
B)  absolute error: 6 pounds 
relative error: $4.7 \%$ 
C)  absolute error: $- 6$ pounds
relative error: $- 4.7 \%$ 
D)  absolute error: $- 6$ pounds 
 relative error: $- 60 \%$

Question 7

Write the number in scientific notation.
-$0.00949$

Accepted Answer

A)  $9.49 \times 10 ^ { - 4 }$ 
B)  $- 9.49 \times 10 ^ { 3 }$ 
C)  $9.49 \times 10 ^ { - 3 }$ 
D)  $9.49 \times 10 ^ { - 2 }$ 
A)  $9.49 \times 10 ^ { - 4 }$ 
B)  $- 9.49 \times 10 ^ { 3 }$ 
C)  $9.49 \times 10 ^ { - 3 }$ 
D)  $9.49 \times 10 ^ { - 2 }$

Question 8

Write the number in scientific notation.
-A beam of light can travel from my house to yours in 60 nanoseconds. (the prefix nano means one billionth).

Accepted Answer

A)  $6 \times 10 ^ { - 8 }$ 
B)  $6 \times 10 ^ { - 9 }$ 
C)  $- 6 \times 10 ^ { 8 }$ 
D)  $6 \times 10 ^ { - 7 }$ 
A)  $6 \times 10 ^ { - 8 }$ 
B)  $6 \times 10 ^ { - 9 }$ 
C)  $- 6 \times 10 ^ { 8 }$ 
D)  $6 \times 10 ^ { - 7 }$

Question 9

Carry out the indicated operation and give your answer with the specified number of significant digits.
-$26.4 \times 0.122 ; 3 \text { significant digits }$

Accepted Answer

A) 3.22 
B) 3.221 
C) 3 
D) 3.2 
A) 3.22 
B) 3.221 
C) 3 
D) 3.2

Question 10

Determine ratio of A to B. Round as indicated.
-$A = \$ 96,000$ is the average cost of a home in Town $A$ and $B = \$ 216,000$ is the average cost of a home in Town B. (Round to the nearest hundredth when necessary.)

Accepted Answer

A)  $4.44$ 
B)  $2.25$ 
C)  $0.44$ 
D)  $0.04$ 
A)  $4.44$ 
B)  $2.25$ 
C)  $0.44$ 
D)  $0.04$

Question 11

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
-The total number of gallons of gasoline that will be used by American drivers in a year.

Accepted Answer

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

Question 12

Two measurements are given. Find the absolute difference and then find the relative difference as a percentage. Assumethat the first quantity is the compared value and the second quantity is the reference value. Round answers to the nearesttenth if necessary.
-The population density in country A is 113 people per square mile while in country B, it is 605 people per square mile.

Accepted Answer

A)  Absolute difference: $- 492$ people per square mile Relative difference: $- 8.1 \%$ 
B)  Absolute difference: 492 people per square mile Relative difference: $\mathbf { 4 3 5 . 4 \% }$ 
C)  Absolute difference: $- 492$ people per square mile Relative difference: $- 435.4 \%$ 
D)  Absolute difference: $- 492$ people per square mile Relative difference: $- 81.3 \%$ 
A)  Absolute difference: $- 492$ people per square mile Relative difference: $- 8.1 \%$ 
B)  Absolute difference: 492 people per square mile Relative difference: $\mathbf { 4 3 5 . 4 \% }$ 
C)  Absolute difference: $- 492$ people per square mile Relative difference: $- 435.4 \%$ 
D)  Absolute difference: $- 492$ people per square mile Relative difference: $- 81.3 \%$

Question 13

Determine ratio of A to B. Round as indicated.
-$\mathrm { A } = 24.7 \%$ is the divorce rate in City A
$B = 28.7 \%$ is the divorce rate in City B
(Round to the nearest hundredth when necessary.)

Accepted Answer

A)  $0.09$ 
B)  $8.61$ 
C)  $1.16$ 
D)  $0.86$ 
A)  $0.09$ 
B)  $8.61$ 
C)  $1.16$ 
D)  $0.86$

Question 14

Round to the indicated place value.
-Round to the nearest whole number: 72.8

Accepted Answer

A) 74 
B) 72 
C) 73 
A) 74 
B) 72 
C) 73

Question 15

Use scientific notation to perform the following operations. Leave your answer in scientific notation.
-$\left( 6 \times 10 ^ { - 2 } \right) \div \left( 24 \times 10 ^ { 4 } \right)$

Accepted Answer

A)  $- 2.5 \times 10 ^ { - 7 }$ 
B)  $2.5 \times 10 ^ { - 7 }$ 
C)  $- 2.5 \times 10 ^ { 5 }$ 
D)  $2.5 \times 10 ^ { 5 }$ 
A)  $- 2.5 \times 10 ^ { - 7 }$ 
B)  $2.5 \times 10 ^ { - 7 }$ 
C)  $- 2.5 \times 10 ^ { 5 }$ 
D)  $2.5 \times 10 ^ { 5 }$

Question 16

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
-You estimate the speed of other cars by pulling up behind a car, driving at the same speed,
and looking at your speedometer.

Accepted Answer

Answers may vary. Possible answer
@#LAT-DLM&
You m

Question 17

Write the number in scientific notation.
-8,099,140

Accepted Answer

A)  $8.09914 \times 10 ^ { 7 }$ 
B)  $8.09914 \times 10 ^ { 1 }$ 
C)  $8.09914 \times 10 ^ { 6 }$ 
D)  $8.09914 \times 10 ^ { - 6 }$ 
A)  $8.09914 \times 10 ^ { 7 }$ 
B)  $8.09914 \times 10 ^ { 1 }$ 
C)  $8.09914 \times 10 ^ { 6 }$ 
D)  $8.09914 \times 10 ^ { - 6 }$

Question 18

Use the Consumer Price Index below to answer the question. $$\begin{array}{l}
\text { Average Annual Consumer Price Index (1982-1984 = 100) }\
\begin{array} { c | c | c | c | c | c } 
\text { Year } & \text { CPI } & \text { Year } & \text { CPI } & \text { Year } & \text { CPI } \
\hline 1986 & 109.6 & 1995 & 152.4 & 2004 & 188.9 \
1987 & 113.6 & 1996 & 156.9 & 2005 & 195.3 \
1988 & 118.3 & 1997 & 160.5 & 2006 & 201.6 \
1989 & 124.0 & 1998 & 163.0 & 2007 & 207.3 \
1990 & 130.7 & 1999 & 166.6 & 2008 & 215.3 \
1991 & 136.2 & 2000 & 172.2 & 2009 & 214.5 \
1992 & 140.3 & 2001 & 177.1 & 2010 & 218.1 \
1993 & 144.5 & 2002 & 179.9 & 2011 & 224.9 \
1994 & 148.2 & 2003 & 184.0 & 2012 & 229.6
\end{array}
\end{array}$$
-In 1992, Sue rented out her apartment for $760 per month. In 2000 she charged $800 per
month.
Convert the 1992 price to 2000 dollars. In real terms, how does the actual price in 2000
compare to the price in 1992? Explain your reasoning.

Accepted Answer

The 1992 price in 2000 dollars is $933.

Question 19

Determine ratio of A to B. Round as indicated.
-$A = 4$ and $B = 28$ (Do not round.)

Accepted Answer

A)  7 
B)  $\frac { 1 } { 7 }$ 
C)  $\frac { 4 } { 7 }$ 
D)  4 
A)  7 
B)  $\frac { 1 } { 7 }$ 
C)  $\frac { 4 } { 7 }$ 
D)  4

Question 20

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.
-In his lifetime my grandfather spent $5 \times 10 ^ { 4 }$ hours watching television.

Accepted Answer

A) True 
 B)False

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

Round to the indicated place value. -Round to the nearest thousandth: 4.4136

Measurements are made at two different times. Find the absolute change and then find the percentage change. Roundanswers to the nearest tenth if necessary. -Last year the Mayor of the town of Little Heath had an approval rating of 71%. This year his approval rating had fallen to 21%.

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror. -The average weight of 100 college-age women, found by asking them their weight during interviews conducted at their college.

Find the absolute and relative errors. -Your weight is 127 pounds but the scale indicates that it is 121 pounds.

Write the number in scientific notation. - $0.00949$

Write the number in scientific notation. -A beam of light can travel from my house to yours in 60 nanoseconds. (the prefix nano means one billionth).

Carry out the indicated operation and give your answer with the specified number of significant digits. - $26.4 \times 0.122 ; 3 \text { significant digits }$

Determine ratio of A to B. Round as indicated. - $A = \$ 96,000$ is the average cost of a home in Town $A$ and $B = \$ 216,000$ is the average cost of a home in Town B. (Round to the nearest hundredth when necessary.)

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. -The total number of gallons of gasoline that will be used by American drivers in a year.

Determine ratio of A to B. Round as indicated. - $\mathrm { A } = 24.7 \%$ is the divorce rate in City A $B = 28.7 \%$ is the divorce rate in City B (Round to the nearest hundredth when necessary.)

Round to the indicated place value. -Round to the nearest whole number: 72.8

Use scientific notation to perform the following operations. Leave your answer in scientific notation. - $\left( 6 \times 10 ^ { - 2 } \right) \div \left( 24 \times 10 ^ { 4 } \right)$

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror. -You estimate the speed of other cars by pulling up behind a car, driving at the same speed, and looking at your speedometer.

Write the number in scientific notation. -8,099,140

Determine ratio of A to B. Round as indicated. - $A = 4$ and $B = 28$ (Do not round.)

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. -In his lifetime my grandfather spent $5 \times 10 ^ { 4 }$ hours watching television.

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