Chapter 4.1, Problem 71E

To determine

Convert $-{125}^{0}36\text{'}$ into decimal degree form.

Answer to Problem 71E

  $-{125.6}^0$

Explanation of Solution

Given: The angle $-{125}^{0}36\text{'}$

Concept Used:

Degree is a measure of an angle. One degree is one 360th part of a full circle.

Each degree is split up into 60 parts, each part being 1/60 of a degree. These parts are called minutes.

Each minute is split up into 60 parts, each part being 1/60 of a minute. These parts are called seconds.

One degree is 60 minutes. One minute is 60 seconds. 360 degrees is the same as a complete circle around north-south axis or from the equator.

Relation between degree and minute $60\text{minutes}=1^0$

Relation between Degrees and seconds $3600\sec =1^0$

Calculation:

  $\begin{array}{l}60\text{minutes}=1^0\\ 1\text{minute}\text{=}\frac{1}{60}\mathrm{deg}\\ 36\text{minutes}=36·\frac{1}{60}\mathrm{deg}=\frac{36}{60}\mathrm{deg}=\frac{6}{10}\mathrm{deg}=0.6\mathrm{deg}\\ -{125}^{0}36\text{'}=-{125}^0+36\text{'}=-{125}^0+{0.6}^0=-{125.6}^0\end{array}$

Thus, $-{125}^{0}36\text{'}$ is equal to $-{125.6}^0$