Chapter 4.1, Problem 7E

Solution

To convert: decimal degree into degree. Minutes and second (DMS).

The DMS form is ${118}^{\circ }19\text{'}12\text{'}\text{'}$ .

Given information:

The decimal degree is ${118.32}^{\circ }$ .

Concept Used:

Step involved in the conversion of decimal into DMS

For the degrees use the whole number part of the decimal

For the minutes multiply the remaining decimal by 60. Use the whole number part of the answer as minutes.

For the seconds multiply the new remaining decimal by 60

Calculation:

Here, the whole number is a degree.

So, ${118.32}^{\circ }$ gives you ${118}^{\circ }$ .

Now, multiply the remaining decimal by $60$ .

  $0.32\cdot 60=19.2$

So, the whole number $19$ equals minutes.

Now, multiply the remaining decimal by $60$ .

  $0.2\cdot 60=12$

So, the whole number $12$ equals seconds.

The Decimal degree ${118.32}^{\circ }$ converts to ${118}^{\circ }$ , $19$ minutes and $12$ seconds.

  ${118.32}^{\circ }={118}^{\circ }19\text{'}12\text{'}\text{'}$

Hence, the decimal, minute, and second form is ${118}^{\circ }19\text{'}12\text{'}\text{'}$ .