Question 1

Write each decimal number in scientific notation.
-5,784,900,000 
A) $5.7849 \times 10 ^ { 8 }$
B) $5.7849 \times 10 ^ { 9 }$
C) $5.7849 \times 10 ^ { 10 }$
D) $5.7849 \times 10 ^ { - 9 }$
E) None of these

Accepted Answer

To convert the number 5,784,900,000 to scientific notation, we move the decimal point 9 places to the left, which gives us $5.7849 \times 10^9$.

Question 2

Convert each number into decimal notation.
-$5.61 \times 10 ^ { - 6 }$
A) 0.000000561
B) 0.00000561
C) 0.0000561
D) 0.000561
E) None of these

Accepted Answer

To convert $5.61 \times 10^{-6}$ into decimal notation, you move the decimal point 6 places to the left, because the exponent is -6. This gives you 0.00000561.

Question 3

Write each decimal number in scientific notation.
-0.007048
A) $7.048 \times 10 ^ { - 3 }$
B) $7.048 \times 10 ^ { - 2 }$
C) $70.48 \times 10 ^ { - 3 }$
D) $7.048 \times 10 ^ { 3 }$
E) None of these

Accepted Answer

To convert 0.007048 to scientific notation, we move the decimal point three places to the right, making it $7.048$. Since we moved the decimal to the right, the exponent on the 10 is negative, resulting in $7.048 \times 10^{-3}$.

Question 4

Convert each number into decimal notation. -9.247 times 10⁹ A) 9,247,000,000,000 B) 9,247,000 C) 924,700,000 D) 9,247,000,000 E) None of these

Accepted Answer

9.247 times 10^9 is equal to 9,247,000,000 in decimal notation.

Question 5

Use your calculator to evaluate the following expressions. If the value is
not exact, round your answer to four decimal places.
-$\sqrt { 6 }$
A) $2.4494$
B) $2.4495$
C) $2.45$
D) $2.2361$
E) None of these

Accepted Answer

The answer of Use your calculator to evaluate the following...

Question 6

Use your calculator to evaluate the following expressions. If the value is
not exact, round your answer to four decimal places.
-$\frac { \pi ^ { 2 } } { 4 }$
A) $2.4649$
B) $2.4674$
C) $0.7854$
D) $2.4673$
E) None of these

Accepted Answer

The answer of Use your calculator to evaluate the following...

Question 7

Simplify the following and write your answers in scientific notation.
-$\frac { \left( 9.8 \times 10 ^ { 11 } \right) \left( 2.6 \times 10 ^ { - 12 } \right) } { 22.4 \times 10 ^ { 33 } }$
A) $1.1375 \times 10 ^ { - 33 }$
B) $1.1375 \times 10 ^ { - 34 }$
C) $113.75 \times 10 ^ { - 34 }$
D) $1.1375 \times 10 ^ { 34 }$
E) None of these

Accepted Answer

The expression simplifies to $ \frac{(9.8 \times 2.6) \times 10^{-1}}{22.4 \times 10^{33}} = \frac{25.48 \times 10^{-1}}{22.4 \times 10^{33}} = 1.1375 \times 10^{-34} $.

Question 8

Determine the number of significant digits.
-0.0040307
A) 1
B) 3
C) 6
D) 8
E) None of these

Accepted Answer

The answer of Determine the number of significant digits.
-0.0040307
A) 1
B)...

Question 9

Simplify the following and write your answers in scientific notation.
-$\frac { \left( 11.2 \times 10 ^ { - 5 } \right) \left( 2.4 \times 10 ^ { 6 } \right) } { 12.8 \times 10 ^ { - 8 } }$
A) $2.1 \times 10 ^ { - 9 }$
B) $21 \times 10 ^ { 9 }$
C) $2.1 \times 10 ^ { 10 }$
D) $2.1 \times 10 ^ { 9 }$
E) None of these

Accepted Answer

The answer of Simplify the following and write your answers...

Question 10

Determine the number of significant digits.
-5,200,010
A) 2
B) 3
C) 6
D) 7
E) None of these

Accepted Answer

Significant digits include all non-zero numbers and zeros that are between significant digits or at the end of the number after a decimal point. In 5,200,010, there are 6 significant digits (5, 2, 0, 0, 0, and 1), with the trailing zero not counted because there's no decimal point.

Question 11

Use dimensional analysis to answer the following.
-The winner of a drag race had a time of 4.52 seconds. The length of the track is one quarter mile. Find the approximate Average speed of the winning car. 
A) $3.3 \frac { \text { miles } } { \text { hour } }$
B) $79.6 \frac { \text { miles } } { \text { hour } }$
C) $199 \frac { \text { miles } } { \text { hour } }$
D) $1085 \frac { \text { miles } } { \text { hour } }$
E) None of these

Accepted Answer

To find the average speed, use the formula: speed = distance/time. The distance is 0.25 miles and the time is 4.52 seconds. Convert 4.52 seconds to hours (4.52/3600) and calculate the speed: (0.25 miles) / (4.52/3600 hours) ≈ 199 miles/hour.

Question 12

Find the mean of the following set of data. 21.1.24 min 1.22 min 1.21 min 1.25 min Assume the data above is used to predict the average time it takes a swimmer to complete two laps in a pool. Use the Mean from the data set to compute the absolute error and Relative error if the actual time it takes the swimmer to Complete the two laps is 1.26 minutes. Round to two Decimal places if necessary.
A) Mean: 1.23 min; AE: 0.03 min; RE: ≈ 23.%8
B) Mean: 1.23 min; AE: 0.03 min; RE: ≈ 11.%9
C) Mean: 1.22 min; AE: 0.04 min; RE: ≈ 31.%7
D) Mean: 1.24 min; AE: 0.02 min; RE: ≈ 15.%9
E) None of these

Accepted Answer

Mean = (21.1 + 1.22 + 1.21 + 1.25) / 4 = 1.23 minAbsolute Error (AE) = |1.23 - 1.26| = 0.03 minRelative Error (RE) = (0.03 / 1.26) * 100 ≈ 23.8%

Question 13

Use dimensional analysis to answer the following.
-Assume that a man spends 20 minutes per day in the shower. Approximately how many hours does the man spend in the Shower during his lifetime if his life expectancy is 84 years?
A year has about 365 days, and a day is about 24 hours.
A) 170 hours
B) 10,220 hours
C) 1533 hours
D) 613,200 hours
E) None of these

Accepted Answer

To find the total hours spent in the shower, calculate: 20 minutes/day * 365 days/year * 84 years = 613,200 minutes. Convert minutes to hours: 613,200 minutes / 60 minutes/hour = 10,220 hours.

Quiz 1: Computation

Write each decimal number in scientific notation. -5,784,900,000

Convert each number into decimal notation. - $5.61 \times 10 ^ { - 6 }$

Write each decimal number in scientific notation. -0.007048

Convert each number into decimal notation. -9.247 times 10⁹

Use your calculator to evaluate the following expressions. If the value is not exact, round your answer to four decimal places. - $\sqrt { 6 }$

Use your calculator to evaluate the following expressions. If the value is not exact, round your answer to four decimal places. - $\frac { \pi ^ { 2 } } { 4 }$

Simplify the following and write your answers in scientific notation. - $\frac { \left( 9.8 \times 10 ^ { 11 } \right) \left( 2.6 \times 10 ^ { - 12 } \right) } { 22.4 \times 10 ^ { 33 } }$

Determine the number of significant digits. -0.0040307

Simplify the following and write your answers in scientific notation. - $\frac { \left( 11.2 \times 10 ^ { - 5 } \right) \left( 2.4 \times 10 ^ { 6 } \right) } { 12.8 \times 10 ^ { - 8 } }$

Determine the number of significant digits. -5,200,010

Use dimensional analysis to answer the following. -The winner of a drag race had a time of 4.52 seconds. The length of the track is one quarter mile. Find the approximate Average speed of the winning car.

Use dimensional analysis to answer the following. -Assume that a man spends 20 minutes per day in the shower. Approximately how many hours does the man spend in the Shower during his lifetime if his life expectancy is 84 years? A year has about 365 days, and a day is about 24 hours.

Quiz 1: Computation

Write each decimal number in scientific notation. -5,784,900,000

Convert each number into decimal notation. - 5.61×10−65.61 \times 10 ^ { - 6 }5.61×10−6

Write each decimal number in scientific notation. -0.007048

Convert each number into decimal notation. -9.247 times 109

Use your calculator to evaluate the following expressions. If the value is not exact, round your answer to four decimal places. - 6\sqrt { 6 }6​

Use your calculator to evaluate the following expressions. If the value is not exact, round your answer to four decimal places. - π24\frac { \pi ^ { 2 } } { 4 }4π2​

Simplify the following and write your answers in scientific notation. - (9.8×1011) (2.6×10−12) 22.4×1033\frac { \left( 9.8 \times 10 ^ { 11 } \right) \left( 2.6 \times 10 ^ { - 12 } \right) } { 22.4 \times 10 ^ { 33 } }22.4×1033(9.8×1011) (2.6×10−12) ​