Convert Degrees, Minutes, Seconds to Decimal Degrees -208 degrees 16’20”

$- 208 ° 16' 20''$

Since $208$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $16$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $20$ by $\frac{1}{3600}$ . Add them together.

$208 + 16 \cdot \frac{1}{60} + 20 \cdot \frac{1}{3600}$

Simplify.

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Remove parentheses.

$208 + 16 \cdot \frac{1}{60} + 20 \cdot \frac{1}{3600}$

Simplify each term.

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Cancel the common factor of $4$ .

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Factor $4$ out of $16$ .

$208 + 4 (4) \cdot \frac{1}{60} + 20 \cdot \frac{1}{3600}$

Factor $4$ out of $60$ .

$208 + 4 \cdot 4 \cdot \frac{1}{4 \cdot 15} + 20 \cdot \frac{1}{3600}$

Cancel the common factor.

$208 + 4 \cdot 4 \cdot \frac{1}{4 \cdot 15} + 20 \cdot \frac{1}{3600}$

Rewrite the expression.

$208 + 4 \cdot \frac{1}{15} + 20 \cdot \frac{1}{3600}$

Combine $4$ and $\frac{1}{15}$ .

$208 + \frac{4}{15} + 20 \cdot \frac{1}{3600}$

Cancel the common factor of $20$ .

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Factor $20$ out of $3600$ .

$208 + \frac{4}{15} + 20 \cdot \frac{1}{20 (180)}$

Cancel the common factor.

$208 + \frac{4}{15} + 20 \cdot \frac{1}{20 \cdot 180}$

Rewrite the expression.

$208 + \frac{4}{15} + \frac{1}{180}$

Find the common denominator.

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Write $208$ as a fraction with denominator $1$ .

$\frac{208}{1} + \frac{4}{15} + \frac{1}{180}$

Multiply $\frac{208}{1}$ by $\frac{180}{180}$ .

$\frac{208}{1} \cdot \frac{180}{180} + \frac{4}{15} + \frac{1}{180}$

Multiply $\frac{208}{1}$ and $\frac{180}{180}$ .

$\frac{208 \cdot 180}{180} + \frac{4}{15} + \frac{1}{180}$

Multiply $\frac{4}{15}$ by $\frac{12}{12}$ .

$\frac{208 \cdot 180}{180} + \frac{4}{15} \cdot \frac{12}{12} + \frac{1}{180}$

Combine.

$\frac{208 \cdot 180}{180} + \frac{4 \cdot 12}{15 \cdot 12} + \frac{1}{180}$

Reorder the factors of $15 \cdot 12$ .

$\frac{208 \cdot 180}{180} + \frac{4 \cdot 12}{12 \cdot 15} + \frac{1}{180}$

Multiply $12$ by $15$ .

$\frac{208 \cdot 180}{180} + \frac{4 \cdot 12}{180} + \frac{1}{180}$

Combine fractions.

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Combine fractions with similar denominators.

$\frac{208 \cdot 180 + 4 \cdot 12 + 1}{180}$

Multiply.

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Multiply $208$ by $180$ .

$\frac{37440 + 4 \cdot 12 + 1}{180}$

Multiply $4$ by $12$ .

$\frac{37440 + 48 + 1}{180}$

Simplify the numerator.

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Add $37440$ and $48$ .

$\frac{37488 + 1}{180}$

Add $37488$ and $1$ .

$\frac{37489}{180}$

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

$208.27\overline{2} °$

Convert Degrees, Minutes, Seconds to Decimal Degrees -208 degrees 16’20”

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