Convert Degrees, Minutes, Seconds to Decimal Degrees 49 degrees 20′

$49 ° 20'$

Since $49$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $20$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $0$ by $\frac{1}{3600}$ . Add them together.

$49 + 20 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Simplify.

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Remove parentheses.

$49 + 20 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Simplify each term.

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Cancel the common factor of $20$ .

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Factor $20$ out of $60$ .

$49 + 20 \cdot \frac{1}{20 (3)} + 0 \cdot \frac{1}{3600}$

Cancel the common factor.

$49 + 20 \cdot \frac{1}{20 \cdot 3} + 0 \cdot \frac{1}{3600}$

Rewrite the expression.

$49 + \frac{1}{3} + 0 \cdot \frac{1}{3600}$

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

$49 + \frac{1}{3} + 0$

To write $\frac{49}{1}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{49}{1} \cdot \frac{3}{3} + \frac{1}{3} + 0$

Write each expression with a common denominator of $3$ , by multiplying each by an appropriate factor of $1$ .

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Combine.

$\frac{49 \cdot 3}{1 \cdot 3} + \frac{1}{3} + 0$

Multiply $3$ by $1$ .

$\frac{49 \cdot 3}{3} + \frac{1}{3} + 0$

Combine the numerators over the common denominator.

$\frac{49 \cdot 3 + 1}{3} + 0$

Simplify the numerator.

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Multiply $49$ by $3$ .

$\frac{147 + 1}{3} + 0$

Add $147$ and $1$ .

$\frac{148}{3} + 0$

Add $\frac{148}{3}$ and $0$ .

$\frac{148}{3}$

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

$49.\overline{3} °$

Convert Degrees, Minutes, Seconds to Decimal Degrees 49 degrees 20′

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