Question 1

Write the number in scientific notation.
-$0.05 \times 10 ^ { 6 }$
A) $0.5 \times 10 ^ { 5 }$
B) $5 \times 10 ^ { 8 }$
C) $5 \times 10 ^ { 4 }$
D) $5 \times 10 ^ { < 5 }$

Accepted Answer

To convert $0.05 \times 10^6$ to scientific notation, you move the decimal point in $0.05$ two places to the right to get $5$, and then adjust the exponent on $10$ by subtracting 2 from 6, resulting in $5 \times 10^4$.

Question 2

Write the number in scientific notation.
-8,099,140
A) $8.09914 \times 10 ^ { 7 }$
B) $8.09914 \times 10 ^ { 1 }$
C) $8.09914 \times 10 ^ { 6 }$
D) $8.09914 \times 10 ^ { - 6 }$

Accepted Answer

To convert a number to scientific notation, you move the decimal point to the right of its first non-zero digit. For 8,099,140, the decimal moves 6 places to the left, making it $8.09914 \times 10^6$.

Question 3

Solve for the percentage in the problem. Round to the nearest tenth of a percent.
-$18.93 is % of $175.72.
A)928.3
B)10.8
C)108.0
D)92.8

Accepted Answer

To find what percentage $18.93 is of $175.72, use the formula: (Part/Whole) * 100. So, ($18.93/$175.72) * 100 = 10.77%, which rounds to 10.8%.

Question 4

Decide whether the statement is believable, given the precision with which it is stated.
-Using a meter stick, I measured the length of the kitchen to within 0.0373 centimeters.
A)Believable
B)Not believable at that precision

Accepted Answer

A standard meter stick typically does not offer precision to the hundredth of a centimeter, making a measurement claim of 0.0373 centimeters highly unlikely and not believable.

Question 5

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits.
-At the beginning of last year, the population of your city was 161,000. By the end of the year it had increased by 2481 people. What was the population at the end of the year?
A)163,000
B)160,000
C)163,500
D)163,481

Accepted Answer

The population at the beginning of the year is given to the nearest thousand, and the increase is given to the nearest person. Therefore, the answer should be rounded to the nearest thousand, which is 163,000.

Question 6

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

$5 \times 10^{4}$ hours equals 50,000 hours. Assuming an average lifespan and viewing habits, it's possible for someone to spend this amount of time watching television over many years.

Question 7

True or false?
-If you score 70% on the midterm math exam and 80% on the final exam, your overall score will be
greater than 75%.
Assume that the final counts for 60% of the grade and that the midterm counts for 40% of the grade.

Accepted Answer

The overall score would be (0.4 * 70) + (0.6 * 80) = 28 + 48 = 76%.

Question 8

Find the absolute and relative errors.
-Your credit card applies a finance charge of $31.36. The finance charge should have been $29.69. 
A) absolute error: $\$ 1.67$
relative error: $5.3 \%$

B) absolute error: $- \$ 1.67$
relative error: $- 5.6 \%$

C) absolute error: $\$ 1.67$
relative error: $5.6 \%$

D) absolute error: $\$ 1.67$

relative error: $16.7 \%$

Accepted Answer

The absolute error is the difference between the actual value and the measured value. In this case, the absolute error is $31.36 - $29.69 = $1.67. The relative error is the absolute error divided by the actual value. In this case, the relative error is $1.67 / $29.69 = 5.6%.

Question 9

Write the number in scientific notation.
-$0.008$
A) $8 \times 10 ^ { - 2 }$
B) $8 \times 10 ^ { - 4 }$
C) $8 \times 10 ^ { - 3 }$
D) $- 8 \times 10 ^ { 3 }$

Accepted Answer

To convert 0.008 into scientific notation, we move the decimal point 3 places to the right, making it $8 \times 10^{-3}$.

Question 10

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.
-Yesterday the total number of gallons of gasoline used by people driving cars in the United States was $7 \times 10 ^ { 10 }$

Accepted Answer

The statement does not make sense because $7 \times 10^{10}$ gallons is an unrealistically high amount for a single day, as the U.S. consumes approximately 370 million gallons of gasoline per day.

Question 11

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated.
-Maria's company has 903 employees, Ruth's company has 751 employees. 903 is what percent of 751 ?
A)120.2
B)1.2
C)83.2
D)0.1

Accepted Answer

To find what percent 903 is of 751, divide 903 by 751 and then multiply by 100. $ \frac{903}{751} \times 100 \approx 120.2\%$.

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

Accepted Answer

To find the amount spent on health insurance, calculate 8% of $73,000: $73,000 \times 0.08 = 5,840$.

Question 13

Round to the indicated place value.
-Round to the nearest thousandth: 3.83366
A)3.8337
B)3.835
C)3.833
D)3.834

Accepted Answer

The answer of Round to the indicated place value.
-Round to...

Question 14

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%. 
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: $- 7 \%$

Accepted Answer

The answer of Measurements are made at two different times....

Question 15

Solve the problem.
-In a local election, 36,700 people voted. This was an increase of 5% over the last election. How many people voted in the last election?
A)34,952 people
B)34,865 people
C)38,535 people
D)38,632 people

Accepted Answer

The number of people who voted in the last election can be found by dividing the current number of voters by 1.05 (since a 5% increase is the same as multiplying the previous number by 1.05). So, 36,700 / 1.05 = 34,952 people.

Question 16

Carry out the indicated operation and give your answer with the specified number of significant digits.
-$\left( 7.4 \times 10 ^ { - 7 } \right) \div \left( 7.867 \times 10 ^ { - 2 } \right) ; 3$ significant digits
A) $9 \times 10 ^ { - 6 }$
B) $9.406 \times 10 ^ { - 6 }$
C) $9.4 \times 10 ^ { - 6 }$
D) $9.41 \times 10 ^ { - 6 }$

Accepted Answer

The result of the division is approximately $9.406 \times 10^{-6}$. Rounding this to 3 significant digits gives $9.41 \times 10^{-6}$.

Question 17

Use scientific notation to perform the following operations. Leave your answer in scientific notation.
-$\left( 25 \times 10 ^ { - 8 } \right) \div \left( 5 \times 10 ^ { 4 } \right)$
A) $5.0 \times 10 ^ { - 12 }$
B) $10 \times 10 ^ { - 4 }$
C) $5.0 \times 10 ^ { - 4 }$
D) $10 \times 10 ^ { - 12 }$

Accepted Answer

Divide the coefficients: $25 \div 5 = 5$. Subtract the exponents: $-8 - 4 = -12$. The result is $5.0 \times 10^{-12}$.

Question 18

Round to the indicated place value.
-Round to the nearest hundredth: $20.17458$
A) $20.1746$
B) $20.175$
C) $20.17$
D) $20.18$

Accepted Answer

The answer of Round to the indicated place value.
-Round to...

Question 19

Write as a percent.
-0.004
A)0.4%
B)4%
C)0.0004%
D)0.004%

Accepted Answer

To convert a decimal to a percent, you multiply by 100. So, 0.004 * 100 = 0.4%.

Question 20

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. 
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: $- 81.3 \%$

Accepted Answer

The answer of Two measurements are given. Find the absolute...

Quiz 3: Numbers in the Real World

Write the number in scientific notation. - $0.05 \times 10 ^ { 6 }$

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

Solve for the percentage in the problem. Round to the nearest tenth of a percent. -$18.93 is % of $175.72.

Decide whether the statement is believable, given the precision with which it is stated. -Using a meter stick, I measured the length of the kitchen to within 0.0373 centimeters.

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits. -At the beginning of last year, the population of your city was 161,000. By the end of the year it had increased by 2481 people. What was the population at the end of the year?

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.

True or false? -If you score 70% on the midterm math exam and 80% on the final exam, your overall score will be greater than 75%. Assume that the final counts for 60% of the grade and that the midterm counts for 40% of the grade.

Find the absolute and relative errors. -Your credit card applies a finance charge of $31.36. The finance charge should have been $29.69.

Write the number in scientific notation. - $0.008$

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. -Yesterday the total number of gallons of gasoline used by people driving cars in the United States was $7 \times 10 ^ { 10 }$

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. -Maria's company has 903 employees, Ruth's company has 751 employees. 903 is what percent of 751 ?

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?

Round to the indicated place value. -Round to the nearest thousandth: 3.83366

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%.

Solve the problem. -In a local election, 36,700 people voted. This was an increase of 5% over the last election. How many people voted in the last election?

Carry out the indicated operation and give your answer with the specified number of significant digits. - $\left( 7.4 \times 10 ^ { - 7 } \right) \div \left( 7.867 \times 10 ^ { - 2 } \right) ; 3$ significant digits

Use scientific notation to perform the following operations. Leave your answer in scientific notation. - $\left( 25 \times 10 ^ { - 8 } \right) \div \left( 5 \times 10 ^ { 4 } \right)$

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

Write as a percent. -0.004