Convert Degrees, Minutes, Seconds to Decimal Degrees 14 degrees 10'

$14 ° 10'$

Since $14$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $10$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $0$ by $\frac{1}{3600}$ . Add them together.

$14 + 10 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Simplify.

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Remove parentheses.

$14 + 10 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Simplify each term.

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Cancel the common factor of $10$ .

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Factor $10$ out of $60$ .

$14 + 10 \cdot \frac{1}{10 (6)} + 0 \cdot \frac{1}{3600}$

Cancel the common factor.

$14 + 10 \cdot \frac{1}{10 \cdot 6} + 0 \cdot \frac{1}{3600}$

Rewrite the expression.

$14 + \frac{1}{6} + 0 \cdot \frac{1}{3600}$

Multiply $0$ by $\frac{1}{3600}$ .

$14 + \frac{1}{6} + 0$

To write $\frac{14}{1}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{14}{1} \cdot \frac{6}{6} + \frac{1}{6} + 0$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Combine.

$\frac{14 \cdot 6}{1 \cdot 6} + \frac{1}{6} + 0$

Multiply $6$ by $1$ .

$\frac{14 \cdot 6}{6} + \frac{1}{6} + 0$

Combine the numerators over the common denominator.

$\frac{14 \cdot 6 + 1}{6} + 0$

Simplify the numerator.

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Multiply $14$ by $6$ .

$\frac{84 + 1}{6} + 0$

Add $84$ and $1$ .

$\frac{85}{6} + 0$

Add $\frac{85}{6}$ and $0$ .

$\frac{85}{6}$

Convert the fraction to a decimal by dividing the numerator by the denominator.

$14.1\overline{6} °$

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