Chapter 15, Problem 15.18EAA

To determine

a.

By expressing the following conversion to 4 significant digits.

Answer to Problem 15.18EAA

$35.87\times {10}^{4}watts$.

Explanation of Solution

Given Information:

$340\frac{Btu}{s}$to $watts$.

We know,

$1\frac{Btu}{s}=1055.055watts$.

Therefore,

$340\frac{Btu}{s}=358718.7watts$.

Converting to 4 digits we get,

$340\frac{Btu}{s}=35.87\times {10}^{4}watts$ ……………………………… (Equation (1))

Conclusion:

Equation 1 provides the required conversion in 4 significant digits.

b.

By expressing the following conversion to 4 significant digits.

$\begin{array}{l}60.35radians\\ \end{array}$.

Given Information:

$3458\mathrm{deg}rees$ to $radians$.

We know,

$1\mathrm{deg}ree=\text{0}\text{.017453}radians$.

Therefore,

$3458\mathrm{deg}rees=60.35radians$ ……………………………… (Equation (2))

Conclusion:

Equation 2 provides the required conversion in 4 significant digits.

c.

By expressing the following conversion to 4 significant digits.

$2500\times {10}^{2}squaremeters$.

Given Information:

$25hectares$ to $squaremeters$.

We know,

$1hectare=10000squaremeters$.

Therefore,

$25hectares=250000squaremeters$.

Converting to 4 digits we get,

$25hectares=2500\times {10}^{2}squaremeters$ ……………………………… (Equation (3))

Conclusion:

Equation 3 provides the required conversion in 4 significant digits.

d.

By expressing the following conversion to 4 significant digits.

$\text{17}\text{.90}\times {\text{10}}^{\text{4}}watts$.

Given Information:

$240horsepower$ to $watts$.

We know,

$1horsepower=745.7watts$.

Therefore,

$240horsepower=\text{178968}watts$.

Converting to 4 digits we get,

$240horsepower=\text{17}\text{.90}\times {\text{10}}^{\text{4}}watts$ ……………………………… (Equation (4))

Conclusion:

Equation 4 provides the required conversion in 4 significant digits.

e.

By expressing the following conversion to 4 significant digits.

$\text{2}\text{.442}\times {\text{10}}^{\text{11}}joules$.

Given Information:

$67851.22kwh(kilowatt-hour)$ to $joules$.

We know,

$1kwh(kilowatt-hour)=\text{3600000}joules$.

Therefore,

$67851.22kwh(kilowatt-hour)=\text{2}\text{.442}\times {\text{10}}^{\text{11}}joules$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

f.

By expressing the following conversion to 4 significant digits.

$\begin{array}{l}\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters\\ \end{array}$.

Given Information:

$2\times {10}^{-7}miles$ to $meters$.

We know,

$1mile=\text{1609}\text{.34}meters$.

Therefore,

$2\times {10}^{-7}miles=\text{0}\text{.00032187}meters$.

Converting to 4 digits we get,

$2\times {10}^{-7}miles=\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

g.

By expressing the following conversion to 4 significant digits.

$\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$.

Given Information:

$40mph$ to $km/s$.

We know,

$1mph=\text{0}\text{.000447}km/s$.

Therefore,

$40mph=\text{0}\text{.01788}km/s$.

Converting to 4 digits we get,

$40mph=\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$ ……………………………… (Equation (6))

Conclusion:

Equation 6 provides the required conversion in 4 significant digits.

To determine

b.

By expressing the following conversion to 4 significant digits.

Answer to Problem 15.18EAA

$\begin{array}{l}60.35radians\\ \end{array}$.

Explanation of Solution

Given Information:

$3458\mathrm{deg}rees$ to $radians$.

We know,

$1\mathrm{deg}ree=\text{0}\text{.017453}radians$.

Therefore,

$3458\mathrm{deg}rees=60.35radians$ ……………………………… (Equation (2))

Conclusion:

Equation 2 provides the required conversion in 4 significant digits.

c.

By expressing the following conversion to 4 significant digits.

$2500\times {10}^{2}squaremeters$.

Given Information:

$25hectares$ to $squaremeters$.

We know,

$1hectare=10000squaremeters$.

Therefore,

$25hectares=250000squaremeters$.

Converting to 4 digits we get,

$25hectares=2500\times {10}^{2}squaremeters$ ……………………………… (Equation (3))

Conclusion:

Equation 3 provides the required conversion in 4 significant digits.

d.

By expressing the following conversion to 4 significant digits.

$\text{17}\text{.90}\times {\text{10}}^{\text{4}}watts$.

Given Information:

$240horsepower$ to $watts$.

We know,

$1horsepower=745.7watts$.

Therefore,

$240horsepower=\text{178968}watts$.

Converting to 4 digits we get,

$240horsepower=\text{17}\text{.90}\times {\text{10}}^{\text{4}}watts$ ……………………………… (Equation (4))

Conclusion:

Equation 4 provides the required conversion in 4 significant digits.

e.

By expressing the following conversion to 4 significant digits.

$\text{2}\text{.442}\times {\text{10}}^{\text{11}}joules$.

Given Information:

$67851.22kwh(kilowatt-hour)$ to $joules$.

We know,

$1kwh(kilowatt-hour)=\text{3600000}joules$.

Therefore,

$67851.22kwh(kilowatt-hour)=\text{2}\text{.442}\times {\text{10}}^{\text{11}}joules$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

f.

By expressing the following conversion to 4 significant digits.

$\begin{array}{l}\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters\\ \end{array}$.

Given Information:

$2\times {10}^{-7}miles$ to $meters$.

We know,

$1mile=\text{1609}\text{.34}meters$.

Therefore,

$2\times {10}^{-7}miles=\text{0}\text{.00032187}meters$.

Converting to 4 digits we get,

$2\times {10}^{-7}miles=\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

g.

By expressing the following conversion to 4 significant digits.

$\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$.

Given Information:

$40mph$ to $km/s$.

We know,

$1mph=\text{0}\text{.000447}km/s$.

Therefore,

$40mph=\text{0}\text{.01788}km/s$.

Converting to 4 digits we get,

$40mph=\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$ ……………………………… (Equation (6))

Conclusion:

Equation 6 provides the required conversion in 4 significant digits.

To determine

c.

By expressing the following conversion to 4 significant digits.

Answer to Problem 15.18EAA

$2500\times {10}^{2}squaremeters$.

Explanation of Solution

Given Information:

$25hectares$ to $squaremeters$.

We know,

$1hectare=10000squaremeters$.

Therefore,

$25hectares=250000squaremeters$.

Converting to 4 digits we get,

$25hectares=2500\times {10}^{2}squaremeters$ ……………………………… (Equation (3))

Conclusion:

Equation 3 provides the required conversion in 4 significant digits.

d.

By expressing the following conversion to 4 significant digits.

$\text{17}\text{.90}\times {\text{10}}^{\text{4}}watts$.

Given Information:

$240horsepower$ to $watts$.

We know,

$1horsepower=745.7watts$.

Therefore,

$240horsepower=\text{178968}watts$.

Converting to 4 digits we get,

$240horsepower=\text{17}\text{.90}\times {\text{10}}^{\text{4}}watts$ ……………………………… (Equation (4))

Conclusion:

Equation 4 provides the required conversion in 4 significant digits.

e.

By expressing the following conversion to 4 significant digits.

$\text{2}\text{.442}\times {\text{10}}^{\text{11}}joules$.

Given Information:

$67851.22kwh(kilowatt-hour)$ to $joules$.

We know,

$1kwh(kilowatt-hour)=\text{3600000}joules$.

Therefore,

$67851.22kwh(kilowatt-hour)=\text{2}\text{.442}\times {\text{10}}^{\text{11}}joules$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

f.

By expressing the following conversion to 4 significant digits.

$\begin{array}{l}\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters\\ \end{array}$.

Given Information:

$2\times {10}^{-7}miles$ to $meters$.

We know,

$1mile=\text{1609}\text{.34}meters$.

Therefore,

$2\times {10}^{-7}miles=\text{0}\text{.00032187}meters$.

Converting to 4 digits we get,

$2\times {10}^{-7}miles=\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

g.

By expressing the following conversion to 4 significant digits.

$\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$.

Given Information:

$40mph$ to $km/s$.

We know,

$1mph=\text{0}\text{.000447}km/s$.

Therefore,

$40mph=\text{0}\text{.01788}km/s$.

Converting to 4 digits we get,

$40mph=\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$ ……………………………… (Equation (6))

Conclusion:

Equation 6 provides the required conversion in 4 significant digits.

To determine

d.

By expressing the following conversion to 4 significant digits.

Answer to Problem 15.18EAA

$\text{17}\text{.90}\times {\text{10}}^{\text{4}}watts$.

Explanation of Solution

Given Information:

$240horsepower$ to $watts$.

We know,

$1horsepower=745.7watts$.

Therefore,

$240horsepower=\text{178968}watts$.

Converting to 4 digits we get,

$240horsepower=\text{17}\text{.90}\times {\text{10}}^{\text{4}}watts$ ……………………………… (Equation (4))

Conclusion:

Equation 4 provides the required conversion in 4 significant digits.

e.

By expressing the following conversion to 4 significant digits.

$\text{2}\text{.442}\times {\text{10}}^{\text{11}}joules$.

Given Information:

$67851.22kwh(kilowatt-hour)$ to $joules$.

We know,

$1kwh(kilowatt-hour)=\text{3600000}joules$.

Therefore,

$67851.22kwh(kilowatt-hour)=\text{2}\text{.442}\times {\text{10}}^{\text{11}}joules$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

f.

By expressing the following conversion to 4 significant digits.

$\begin{array}{l}\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters\\ \end{array}$.

Given Information:

$2\times {10}^{-7}miles$ to $meters$.

We know,

$1mile=\text{1609}\text{.34}meters$.

Therefore,

$2\times {10}^{-7}miles=\text{0}\text{.00032187}meters$.

Converting to 4 digits we get,

$2\times {10}^{-7}miles=\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

g.

By expressing the following conversion to 4 significant digits.

$\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$.

Given Information:

$40mph$ to $km/s$.

We know,

$1mph=\text{0}\text{.000447}km/s$.

Therefore,

$40mph=\text{0}\text{.01788}km/s$.

Converting to 4 digits we get,

$40mph=\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$ ……………………………… (Equation (6))

Conclusion:

Equation 6 provides the required conversion in 4 significant digits.

To determine

e.

By expressing the following conversion to 4 significant digits.

Answer to Problem 15.18EAA

$\text{2}\text{.442}\times {\text{10}}^{\text{11}}joules$.

Explanation of Solution

Given Information:

$67851.22kwh(kilowatt-hour)$ to $joules$.

We know,

$1kwh(kilowatt-hour)=\text{3600000}joules$.

Therefore,

$67851.22kwh(kilowatt-hour)=\text{2}\text{.442}\times {\text{10}}^{\text{11}}joules$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

f.

By expressing the following conversion to 4 significant digits.

$\begin{array}{l}\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters\\ \end{array}$.

Given Information:

$2\times {10}^{-7}miles$ to $meters$.

We know,

$1mile=\text{1609}\text{.34}meters$.

Therefore,

$2\times {10}^{-7}miles=\text{0}\text{.00032187}meters$.

Converting to 4 digits we get,

$2\times {10}^{-7}miles=\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

g.

By expressing the following conversion to 4 significant digits.

$\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$.

Given Information:

$40mph$ to $km/s$.

We know,

$1mph=\text{0}\text{.000447}km/s$.

Therefore,

$40mph=\text{0}\text{.01788}km/s$.

Converting to 4 digits we get,

$40mph=\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$ ……………………………… (Equation (6))

Conclusion:

Equation 6 provides the required conversion in 4 significant digits.

To determine

f.

By expressing the following conversion to 4 significant digits.

Answer to Problem 15.18EAA

$\begin{array}{l}\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters\\ \end{array}$.

Explanation of Solution

Given Information:

$2\times {10}^{-7}miles$ to $meters$.

We know,

$1mile=\text{1609}\text{.34}meters$.

Therefore,

$2\times {10}^{-7}miles=\text{0}\text{.00032187}meters$.

Converting to 4 digits we get,

$2\times {10}^{-7}miles=\text{3}\text{.218}\times {\text{10}}^{\text{-4}}meters$ ……………………………… (Equation (5))

Conclusion:

Equation 5 provides the required conversion in 4 significant digits.

g.

By expressing the following conversion to 4 significant digits.

$\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$.

Given Information:

$40mph$ to $km/s$.

We know,

$1mph=\text{0}\text{.000447}km/s$.

Therefore,

$40mph=\text{0}\text{.01788}km/s$.

Converting to 4 digits we get,

$40mph=\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$ ……………………………… (Equation (6))

Conclusion:

Equation 6 provides the required conversion in 4 significant digits.

To determine

g.

By expressing the following conversion to 4 significant digits.

Answer to Problem 15.18EAA

$\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$.

Explanation of Solution

Given Information:

$40mph$ to $km/s$.

We know,

$1mph=\text{0}\text{.000447}km/s$.

Therefore,

$40mph=\text{0}\text{.01788}km/s$.

Converting to 4 digits we get,

$40mph=\text{1}\text{.788}\times {\text{10}}^{\text{-2}}km/s$ ……………………………… (Equation (6))

Conclusion:

Equation 6 provides the required conversion in 4 significant digits.