# How do you convert -145.8^circ to D^circM'S'' form?

May 8, 2017

Strip off the numbers to the right of the decimal and convert those to minutes.
Strip off the numbers to the right of the decimal of the converted minutes and convert those to seconds.

#### Explanation:

Strip off the number(s) to the right of the decimal and perform dimensional conversion on it.

We start the dimensional conversion by writing the value over 1:

${0.8}^{\circ} / 1$

Multiply by the factor for converting from degrees to minutes:

${0.8}^{\circ} / 1 \frac{60 \text{'}}{1} ^ \circ$

Please observe that the units of degrees cancel:

${0.8}^{\cancel{\circ}} / 1 \frac{60 '}{1} ^ \cancel{\circ} = 48 '$

If there were numbers to the right of the decimal, we would strip those off and convert them to seconds, using the factor $\frac{60 ' '}{1 '}$ but this is not the case.

$- {145.8}^{\circ} = {145}^{\circ} 48 '$

May 8, 2017

$- {145}^{\circ} 48 ' 0 ' '$

#### Explanation:

You need to know the conversion: ${1}^{\circ} = 60 ' = 3600 ' '$.

Given: $- {145.8}^{\circ}$

The ${D}^{\circ} =$the integer portion of the decimal degree:

${D}^{\circ} = - 145$

The Minute, $M$ = the integer portion of the decimal portion multiplied by 60:

$M = 0.8 \cdot 60 = 48.0 '$

The Second, $S$ = the integer portion of the minute decimal portion (the zero of $48.0$) multiplied by $60$:

$S = 0.0 \cdot 60 = 0 ' '$

$- {145.8}^{\circ} = - {145}^{\circ} 48 ' 0 ' '$