Question 1

State the number of significant digits and the implied precision of the given number.
-2200.0

Accepted Answer

A) 5 significant digits, precise to the nearest tenth 
B) 3 significant digits, precise to the nearest tenth 
C) 5 significant digits, precise to the nearest 100 
D) 2 significant digits, precise to the nearest 100 
A) 5 significant digits, precise to the nearest tenth 
B) 3 significant digits, precise to the nearest tenth 
C) 5 significant digits, precise to the nearest 100 
D) 2 significant digits, precise to the nearest 100

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.
-The total rainfall in Laketown last year was 8.8 inches. This year it was 0.7 inches.

Accepted Answer

A)  Absolute change: $- 8.1$ in.
Percentage change: $- 1157.1 \%$ 
B)  Absolute change: $- 8.1$ in.
Percentage change: $- 92 \%$ 
C)  Absolute change: $8.1$ in.
Percentage change: $1157.1 \%$ 
D)  Absolute change: $- 8.1$ in.

Percentage change: $- 9.2 \%$ 
A)  Absolute change: $- 8.1$ in.
Percentage change: $- 1157.1 \%$ 
B)  Absolute change: $- 8.1$ in.
Percentage change: $- 92 \%$ 
C)  Absolute change: $8.1$ in.
Percentage change: $1157.1 \%$ 
D)  Absolute change: $- 8.1$ in.

Percentage change: $- 9.2 \%$

Question 3

Write the percentage as a fraction or decimal, as indicated.
-Write as a fraction.
$0.05 \%$

Accepted Answer

A)  $\frac { 1 } { 4000 }$ 
B)  $\frac { 1 } { 200 }$ 
C)  $\frac { 1 } { 2000 }$ 
D)  $\frac { 1 } { 1000 }$ 
A)  $\frac { 1 } { 4000 }$ 
B)  $\frac { 1 } { 200 }$ 
C)  $\frac { 1 } { 2000 }$ 
D)  $\frac { 1 } { 1000 }$

Question 4

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 200 exercise regularly and 100 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 100 exercise regularly and 200 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 21.6%.
Explain the apparent inconsistency in these results.

Accepted Answer

A) Among those who exercise regularly, younger people have a lower rate of high blood pressure, and among those who do not exercise regularly younger people have a lower rate of
High blood pressure. But looking at both groups combined, young people have a higher rate
Of high blood pressure. 
B) In spite of exercising, people get older. 
C) Within each age group the percentage with high blood pressure is lower amongst those who exercise, but when the age groups are combined, the percentage with high blood pressure is
Higher amongst those who exercise. 
D) Within the under-40 age group the percentage with high blood pressure is lower amongst those who exercise, but within the over-40 age group, the percentage with high blood
Pressure is higher amongst those who exercise. 
A) Among those who exercise regularly, younger people have a lower rate of high blood pressure, and among those who do not exercise regularly younger people have a lower rate of
High blood pressure. But looking at both groups combined, young people have a higher rate
Of high blood pressure. 
B) In spite of exercising, people get older. 
C) Within each age group the percentage with high blood pressure is lower amongst those who exercise, but when the age groups are combined, the percentage with high blood pressure is
Higher amongst those who exercise. 
D) Within the under-40 age group the percentage with high blood pressure is lower amongst those who exercise, but within the over-40 age group, the percentage with high blood
Pressure is higher amongst those who exercise.

Question 5

Write the number in scientific notation.
-$302.23$

Accepted Answer

A)  $3.0223 \times 10 ^ { - 2 }$ 
B)  $3.0223 \times 10 ^ { 2 }$ 
C)  $3.0223 \times 10 ^ { - 3 }$ 
D)  $3.0223 \times 10 ^ { 3 }$ 
A)  $3.0223 \times 10 ^ { - 2 }$ 
B)  $3.0223 \times 10 ^ { 2 }$ 
C)  $3.0223 \times 10 ^ { - 3 }$ 
D)  $3.0223 \times 10 ^ { 3 }$

Question 6

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.
-Last year the total revenue for Clearline phone company was $13.7 million while the revenue for its competitor, the Speakmore was $10.8 million.

Accepted Answer

A)  Absolute difference: $\$ 2.9$ million
Relative difference: $2.7 \%$ 
B)  Absolute difference: $\$ 2.9$ million
 Relative difference: $21.2 \%$ 
C)  Absolute difference: $\$ 2.9$ million
 Relative difference: $26.9 \%$ 
D)  Absolute difference: $\$ - 2.9$ million
 Relative difference: $- 21.2 \%$ 
A)  Absolute difference: $\$ 2.9$ million
Relative difference: $2.7 \%$ 
B)  Absolute difference: $\$ 2.9$ million
 Relative difference: $21.2 \%$ 
C)  Absolute difference: $\$ 2.9$ million
 Relative difference: $26.9 \%$ 
D)  Absolute difference: $\$ - 2.9$ million
 Relative difference: $- 21.2 \%$

Question 7

Solve the problem.
-During the sale the price of the sofa was discounted by 15%. Determine which of the statement's below is true.

Accepted Answer

A) The sale price of the sofa is 85% less than the regular price. 
B) The sale price of the sofa is 85% of the regular price. 
C) The sale price of the sofa is 15% of the regular price. 
D) The regular price of the sofa is 101% of the sale price. 
A) The sale price of the sofa is 85% less than the regular price. 
B) The sale price of the sofa is 85% of the regular price. 
C) The sale price of the sofa is 15% of the regular price. 
D) The regular price of the sofa is 101% of the sale price.

Question 8

Use scientific notation to solve the problem.
-The distance from the earth to the sun is 92,900,000 miles. How long would it take a rocket, traveling a $2.9 \times 10 ^ { 3 }$ miles per hour, to reach the sun?

Accepted Answer

A)  $3.2 \times 10 ^ { 4 } \mathrm { hr }$ 
B)  $3.2 \times 10 ^ { 2 } \mathrm { hr }$ 
C)  $3.2 \times 10 ^ { 3 } \mathrm { hr }$ 
D)  $3.2 \mathrm { hr }$ 
A)  $3.2 \times 10 ^ { 4 } \mathrm { hr }$ 
B)  $3.2 \times 10 ^ { 2 } \mathrm { hr }$ 
C)  $3.2 \times 10 ^ { 3 } \mathrm { hr }$ 
D)  $3.2 \mathrm { hr }$

Question 9

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
-According to police reports, attendance at the last three anti-war rallies was 45,000, 60,000,
and 22,300 respectively.

Accepted Answer

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

Question 10

State the number of significant digits and the implied precision of the given number.
-4500

Accepted Answer

A) 2 significant digits, precise to the nearest 100 
B) 4 significant digits, precise to the nearest unit 
C) 2 significant digits, precise to the nearest 1000 
D) 4 significant digits, precise to the nearest 100 
A) 2 significant digits, precise to the nearest 100 
B) 4 significant digits, precise to the nearest unit 
C) 2 significant digits, precise to the nearest 1000 
D) 4 significant digits, precise to the nearest 100

Question 11

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

Accepted Answer

A)  $- 2,116,000$ 
B)  $0.00002116$ 
C)  $0.0000002116$ 
D)  $0.000002116$ 
A)  $- 2,116,000$ 
B)  $0.00002116$ 
C)  $0.0000002116$ 
D)  $0.000002116$

Question 12

Solve the problem.
-An outlet store had monthly sales of $73,000 and spent 8% of it on health insurance. How much was spent on health insurance?

Accepted Answer

A) $912,500 
B) $91,250 
C) $58,400 
D) $5840 
A) $912,500 
B) $91,250 
C) $58,400 
D) $5840

Question 13

Answer the question.
-Find the scale ratio for a map if 6 inches on the map represents 7 miles on the ground.

Accepted Answer

A) 1 : 6160 
B) 1 : 443,520 
C) 1 : 73,920 
D) 1 : 10,560 
A) 1 : 6160 
B) 1 : 443,520 
C) 1 : 73,920 
D) 1 : 10,560

Question 14

Write the percentage as a fraction or decimal, as indicated.
-Write as a fraction. 7.625%

Accepted Answer

A)  $\frac { 61 } { 400 }$ 
B)  $\frac { 61 } { 800 }$ 
C)  $\frac { 61 } { 1600 }$ 
D)  $\frac { 61 } { 80 }$ 
A)  $\frac { 61 } { 400 }$ 
B)  $\frac { 61 } { 800 }$ 
C)  $\frac { 61 } { 1600 }$ 
D)  $\frac { 61 } { 80 }$

Question 15

Determine whether the source of error represents random or systematic error.
-When scientists estimate the height of a mountain there is a certain amount of error involved in measuring distances and angles.

Accepted Answer

A) Systematic error 
B) Random error 
A) Systematic error 
B) Random error

Question 16

Write the number in scientific notation.
-$0.008$

Accepted Answer

A)  $8 \times 10 ^ { - 2 }$ 
B)  $8 \times 10 ^ { - 4 }$ 
C)  $8 \times 10 ^ { - 3 }$ 
D)  $- 8 \times 10 ^ { 3 }$ 
A)  $8 \times 10 ^ { - 2 }$ 
B)  $8 \times 10 ^ { - 4 }$ 
C)  $8 \times 10 ^ { - 3 }$ 
D)  $- 8 \times 10 ^ { 3 }$

Question 17

Determine whether the source of error represents random or systematic error.
-A survey is conducted on smoking amongst teenagers. When questioned by adults, teenagers tend to underreport how much they smoke.

Accepted Answer

A) Random error 
B) Systematic error 
A) Random error 
B) Systematic error

Question 18

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) True 
 B)False

Question 19

Write the number in ordinary notation.
-$6.96 \times 10 ^ { 4 }$

Accepted Answer

A)  696,000 
B)  69,600 
C)  6960 
D)  $278.4$ 
A)  696,000 
B)  69,600 
C)  6960 
D)  $278.4$

Question 20

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.

Accepted Answer

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: $4.8 \%$ 
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: $4.8 \%$

State the number of significant digits and the implied precision of the given number. -2200.0

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 total rainfall in Laketown last year was 8.8 inches. This year it was 0.7 inches.

Write the percentage as a fraction or decimal, as indicated. -Write as a fraction. $0.05 \%$

Write the number in scientific notation. - $302.23$

Solve the problem. -During the sale the price of the sofa was discounted by 15%. Determine which of the statement's below is true.

Use scientific notation to solve the problem. -The distance from the earth to the sun is 92,900,000 miles. How long would it take a rocket, traveling a $2.9 \times 10 ^ { 3 }$ miles per hour, to reach the sun?

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror. -According to police reports, attendance at the last three anti-war rallies was 45,000, 60,000, and 22,300 respectively.

State the number of significant digits and the implied precision of the given number. -4500

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

Solve the problem. -An outlet store had monthly sales of $73,000 and spent 8% of it on health insurance. How much was spent on health insurance?

Answer the question. -Find the scale ratio for a map if 6 inches on the map represents 7 miles on the ground.

Write the percentage as a fraction or decimal, as indicated. -Write as a fraction. 7.625%

Determine whether the source of error represents random or systematic error. -When scientists estimate the height of a mountain there is a certain amount of error involved in measuring distances and angles.

Write the number in scientific notation. - $0.008$

Determine whether the source of error represents random or systematic error. -A survey is conducted on smoking amongst teenagers. When questioned by adults, teenagers tend to underreport how much they smoke.

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. - $6.96 \times 10 ^ { 4 }$

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.

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