Chapter 1.1, Problem 1E

(Practice) a. To convert inches (in) to feet (ft), the number of inches should be multiplied by which of the following conversion factors?
i. 12 in/1 ft   ii. 1 ft/12 in
b. To convert feet (ft) to meters (m), the number of feet should be multiplied by which of the following conversion factors?
i. 1 m/3.28 ft   ii. 3.28 ft/1 m
c. To convert sq.yd to sq.ft, the number of sq.yd should be multiplied by which of the following conversion factors?
i. 1 sq.yd/9 sq.ft   ii. 9 sq.ft/1 sq.yd
d. To convert meters (m) to kilometers (km), the number of meters should be multiplied by which of the following conversion factors?
i. 1000 m/1 km   ii. 1 km/1000 m
e. To convert sq.in to sq.ft, the number of sq.in should be multiplied by which of the following conversion factors?
i. 144 sq.in/1 sq.ft   ii. 1 sq.ft/144 sq.in
f. To convert minutes (min) to seconds (sec), the number of minutes should be multiplied by which of the following conversion factors?
i. 60 sec/1 min   ii. 1 min/60 sec
g. To convert seconds (sec) to minutes (min), the number of seconds should be multiplied by which of the following conversion factors?
i. 60 sec/1 min   ii. 1 min/60 sec

Program Plan Intro

To determine the correct option to be multiplied with the number of inches, to convert inches into feet.

Program Description Answer

Option ii) 1ft/12 in correct.

Explanation of Solution

Explanation

Normally, $1in=\frac{1}{12}ft$

Checking both the given option by multiplying it with 1 inch, and if we get the above given expression then the generated result is true.

i) $\frac{12\text{ in}}{1\text{ ft}}$ ,

  $1in\times \frac{12\text{ in}}{1\text{ ft}}=\frac{12i{n}^2}{1\text{ f}t}$ .

This option is false.

ii) $\frac{1\text{ ft}}{12\text{ in}}$

  $1\cancel{in}\times \frac{1\text{ ft}}{12\cancel{\text{in}}}=\frac{1\text{ f}t}{12}$

This option is true.

Conclusion

Hence, the option ii) is correct.

Program Plan Intro

To determine the correct option to be multiplied with the number of feet, to convert feet into meters.

Program Description Answer

The option i) 1m/3.28 ftis correct.

Explanation of Solution

Explanation

Normally, $1\text{ ft=0}\text{.3048 m}$

Checking both the given option by multiplying it with 1 feet, and if we get the above given expression then the generated result is true.

i) $\frac{1\text{ m}}{3.28\text{ ft}}$ ,

  $1\cancel{\text{ft}}\times \frac{1\text{ m}}{3.28\cancel{\text{ft}}}=\frac{1\text{ m}}{3.28}=0.3048m$ .

This option is true.

ii) $\frac{3.28\text{ ft}}{1\text{ m}}$

  $1\text{ ft}\times \frac{3.28\text{ ft}}{1\text{ m}}=\frac{\text{3}\text{.28 f}{t}^2}{1m}$

This option is false.

Conclusion

Hence, the option i) is correct.

Program Plan Intro

To determine the correct option to be multiplied with the number of sq. yd, to convert sq. yd into sq. ft.

Program Description Answer

The option ii) $\frac{\text{9 sq}\text{.ft}}{1\text{ sq}\text{. yd}}$ is correct.

Explanation of Solution

Explanation

Normally, $1\text{ sq}\text{. yd=9 sq}\text{. ft}$

Checking both the given option by multiplying it with 1 sq. yd, and if we get the above given expression then the generated result is true.

i) $\frac{1\text{ sq}\text{. yd}}{9\text{ sq}\text{. ft}}$ ,

  $1\text{ sq}\text{. yd}\times \frac{1\text{ sq}\text{. yd}}{9\text{ sq}\text{. ft}}=\frac{1{\left(\text{sq}\text{. yd}\right)}^{\text{2}}}{9\text{ sq}\text{. ft}}$ .

This option is false.

ii) $\frac{\text{9 sq}\text{.ft}}{1\text{ sq}\text{. yd}}$

  $1\cancel{\text{sq}\text{. yd}}\times \frac{\text{9 sq}\text{.ft}}{1\cancel{\text{sq}\text{. yd}}}=\text{9 sq}\text{.ft}$

This option is true.

Conclusion

Hence, the option ii) is true.

Program Plan Intro

To determine the correct option to be multiplied with the number of meters, to convert metres(m) into kilometer(km).

Program Description Answer

The option ii) $\frac{1km}{1000m}$ is correct.

Explanation of Solution

Explanation

Normally, $1\text{ m=}\frac{\text{1}}{1000}\text{ km}$

Checking both the given option by multiplying it with 1 m, and if we get the above given expression then the generated result is true.

i) $1000m/1km$ ,

  $1\text{ m}\times \frac{1000m}{1km}=\frac{1000m^2}{1\text{km}}$ .

This option is false.

ii) $\frac{1km}{1000m}$

  $1\cancel{m}\times \frac{1km}{1000\cancel{m}}=\frac{1}{1000}km$

This option is true.

Conclusion

Hence, the option ii) is true.

Program Plan Intro

To determine the correct option to be multiplied with the number of sq. in, to convert sq. ft into sq. ft.

Program Description Answer

The option ii) $\frac{1sq.ft}{144\text{ sq}\text{. in}}$ is correct.

Explanation of Solution

Explanation

Normally, $1\text{ sq}\text{. in=0}\text{.0069 sq}\text{. ft}$

Checking both the given option by multiplying it with 1 sq. in, and if we get the above given expression then the generated result is true.

i) $\frac{144sq.in}{1\text{ sq}\text{. ft}}$ ,

  $1\text{ sq}\text{. in}\times \frac{144sq.in}{1\text{ sq}\text{. ft}}=\frac{144{\left(sq.in\right)}^2}{1\text{ sq}\text{. ft }}$ .

This option is false.

ii) $\frac{1sq.ft}{144\text{ sq}\text{. in}}$

  $1\cancel{\text{sq}\text{. in}}\times \frac{1sq.ft}{144\cancel{\text{sq}\text{. in}}}=\frac{1}{144}sq.feet$

This option is true.

Conclusion

Hence, the option ii) is true.

Program Plan Intro

To determine the correct option to be multiplied with the number of minutes, to convert minutes(min) into seconds(sec).

Program Description Answer

The option i) $\frac{60\sec }{1\text{ min}}$ is correct.

Explanation of Solution

Explanation

Normally, $1\text{ min=60 sec}$

Checking both the given option by multiplying it with 1 min, and if we get the above given expression then the generated result is true.

i) $\frac{60\sec }{1\text{ min}}$ ,

  $1\cancel{\text{min}}\times \frac{60\sec }{1\cancel{\text{min}}}=60\sec$ .

This option is true.

ii) $\frac{1\min }{60\text{ sec}}$

  $1\text{ min}\times \frac{1\min }{60\text{ sec}}=\frac{1{\min }^2}{60\sec }$

This option is false.

Conclusion

Hence, the option i) is true.

Program Plan Intro

To determine the correct option to be multiplied with the number of seconds, to convert seconds(sec) into minutes(min).

Program Description Answer

The option ii) $\frac{1\min }{60\text{ sec}}$ is

correct.

Explanation of Solution

Explanation

Normally, $1\text{ sec=}\frac{1}{60}\min$

Checking both the given option by multiplying it with 1 sec, and if we get the above given expression then the generated result is

true.

i) $\frac{60\sec }{1\text{ min}}$ ,

  $1\text{ sec}\times \frac{60\sec }{1\text{ min}}=\frac{60{\sec }^2}{1\min }$ .

This option is false.

ii) $\frac{1\min }{60\text{ sec}}$

  $1\cancel{\text{sec}}\times \frac{1\min }{60\cancel{\text{sec}}}=\frac{1}{60}\min$

This option is true.

Conclusion

Hence, the option ii) is true.