# How do we write 1440/13 degrees in minutes and seconds?

Mar 8, 2017

$\frac{1440}{13}$ degrees are ${110}^{\circ} 46 ' 9.23 ' '$

#### Explanation:

Before we attempt this, recalling

we have $60 '$ called sixty minutes in each degree

and $60 ' '$ called sixty seconds in each minute.

As $\frac{1440}{13} = 110 + \frac{10}{13}$ degrees which we can write as ${110}^{\circ}$ and ${\left(\frac{10}{13}\right)}^{\circ}$

Now converting ${\left(\frac{10}{13}\right)}^{\circ}$ into minutes we have

${\left(\frac{10}{13}\right)}^{\circ} = \frac{10}{13} \times 60 = \frac{600}{13} = 46 \frac{2}{13}$ minutes and we can write it as $46 '$ and $\left(\frac{2}{13}\right) '$

and $\left(\frac{2}{13}\right) '$ are $\frac{2}{13} \times 60 = \frac{120}{13} = 9.23$ seconds.

Hence $\frac{1440}{13}$ degrees are ${110}^{\circ} 46 ' 9.23 ' '$