Precalculus Examples

$39 ° 6'$

Step 1

Since $39$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $6$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $0$ by $\frac{1}{3600}$ . Add them together.

$39 + 6 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$39 + 6 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Factor $6$ out of $60$ .

$39 + 6 \cdot \frac{1}{6 (10)} + 0 \cdot \frac{1}{3600}$

Step 2.2.1.2

Cancel the common factor.

$39 + 6 \cdot \frac{1}{6 \cdot 10} + 0 \cdot \frac{1}{3600}$

Step 2.2.1.3

Rewrite the expression.

$39 + \frac{1}{10} + 0 \cdot \frac{1}{3600}$

Step 2.2.2

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

$39 + \frac{1}{10} + 0$

Step 2.3

To write $39$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$39 \cdot \frac{10}{10} + \frac{1}{10} + 0$

Step 2.4

Combine $39$ and $\frac{10}{10}$ .

$\frac{39 \cdot 10}{10} + \frac{1}{10} + 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{39 \cdot 10 + 1}{10} + 0$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $39$ by $10$ .

$\frac{390 + 1}{10} + 0$

Step 2.6.2

Add $390$ and $1$ .

$\frac{391}{10} + 0$

Step 2.7

Add $\frac{391}{10}$ and $0$ .

$\frac{391}{10}$

Step 3

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

$39.1 °$