Precalculus Examples

$48 ° 30' 36''$

Step 1

Since $48$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $30$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $36$ by $\frac{1}{3600}$ . Add them together.

$48 + 30 \cdot \frac{1}{60} + 36 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$48 + 30 \cdot \frac{1}{60} + 36 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $30$ .

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Step 2.2.1.1

Factor $30$ out of $60$ .

$48 + 30 \cdot \frac{1}{30 (2)} + 36 \cdot \frac{1}{3600}$

Step 2.2.1.2

Cancel the common factor.

$48 + 30 \cdot \frac{1}{30 \cdot 2} + 36 \cdot \frac{1}{3600}$

Step 2.2.1.3

Rewrite the expression.

$48 + \frac{1}{2} + 36 \cdot \frac{1}{3600}$

Step 2.2.2

Cancel the common factor of $36$ .

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Step 2.2.2.1

Factor $36$ out of $3600$ .

$48 + \frac{1}{2} + 36 \cdot \frac{1}{36 (100)}$

Step 2.2.2.2

Cancel the common factor.

$48 + \frac{1}{2} + 36 \cdot \frac{1}{36 \cdot 100}$

Step 2.2.2.3

Rewrite the expression.

$48 + \frac{1}{2} + \frac{1}{100}$

Step 2.3

Find the common denominator.

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Step 2.3.1

Write $48$ as a fraction with denominator $1$ .

$\frac{48}{1} + \frac{1}{2} + \frac{1}{100}$

Step 2.3.2

Multiply $\frac{48}{1}$ by $\frac{100}{100}$ .

$\frac{48}{1} \cdot \frac{100}{100} + \frac{1}{2} + \frac{1}{100}$

Step 2.3.3

Multiply $\frac{48}{1}$ by $\frac{100}{100}$ .

$\frac{48 \cdot 100}{100} + \frac{1}{2} + \frac{1}{100}$

Step 2.3.4

Multiply $\frac{1}{2}$ by $\frac{50}{50}$ .

$\frac{48 \cdot 100}{100} + \frac{1}{2} \cdot \frac{50}{50} + \frac{1}{100}$

Step 2.3.5

Multiply $\frac{1}{2}$ by $\frac{50}{50}$ .

$\frac{48 \cdot 100}{100} + \frac{50}{2 \cdot 50} + \frac{1}{100}$

Step 2.3.6

Multiply $2$ by $50$ .

$\frac{48 \cdot 100}{100} + \frac{50}{100} + \frac{1}{100}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{48 \cdot 100 + 50 + 1}{100}$

Step 2.5

Simplify the expression.

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Step 2.5.1

Multiply $48$ by $100$ .

$\frac{4800 + 50 + 1}{100}$

Step 2.5.2

Add $4800$ and $50$ .

$\frac{4850 + 1}{100}$

Step 2.5.3

Add $4850$ and $1$ .

$\frac{4851}{100}$

Step 3

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

$48.51 °$