Chapter 4.1, Problem 50E

a.

To determine

To convert: $345.12°$ to $D°M^{\prime }{S}^{″}$ form

Answer to Problem 50E

  $345°7^{\prime }12^{″}$

Explanation of Solution

To convert a decimal degree to $D°M^{\prime }{S}^{″}$ form, the whole number part of the decimal gives degrees.

Thus, $345.12°$ gives $345°$ .

Next step is to multiply the decimal part by 60 and use the whole part obtained as minutes.

  $0.12\times 60=7.20$

So, the whole number 7 equals minutes.

Next step is to multiply the decimal part by 60 and use the whole part obtained as seconds.

  $0.2\times 60=12.0$

So, the whole number 12 equals seconds.

Thus, $345.12°=345°7^{\prime }12^{″}$

b.

To determine

To convert: $-3.58°$ to $D°M^{\prime }{S}^{″}$ form

Answer to Problem 50E

  $-3°34^{\prime }48^{″}$

Explanation of Solution

To convert a decimal degree to $D°M^{\prime }{S}^{″}$ form, the whole number part of the decimal gives degrees.

Thus, $-3.58°$ gives $-3°$ .

Next step is to multiply the decimal part by and use the whole part obtained as minutes.

  $0.58\times 60=34.8$

So, the whole number 34 equals minutes.

Next step is to multiply the decimal part by 60 and use the whole part obtained as seconds.

  $0.8\times 60=48.0$

So, the whole number 12 equals seconds.

Thus, $-3.58°=-3°34^{\prime }48^{″}$