Precalculus Examples

$8 ° 8' 8''$

Step 1

Since $8$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $8$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $8$ by $\frac{1}{3600}$ . Add them together.

$8 + 8 \cdot \frac{1}{60} + 8 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$8 + 8 \cdot \frac{1}{60} + 8 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Factor $4$ out of $8$ .

$8 + 4 (2) \cdot \frac{1}{60} + 8 \cdot \frac{1}{3600}$

Step 2.2.1.2

Factor $4$ out of $60$ .

$8 + 4 \cdot 2 \cdot \frac{1}{4 \cdot 15} + 8 \cdot \frac{1}{3600}$

Step 2.2.1.3

Cancel the common factor.

$8 + 4 \cdot 2 \cdot \frac{1}{4 \cdot 15} + 8 \cdot \frac{1}{3600}$

Step 2.2.1.4

Rewrite the expression.

$8 + 2 \cdot \frac{1}{15} + 8 \cdot \frac{1}{3600}$

Step 2.2.2

Combine $2$ and $\frac{1}{15}$ .

$8 + \frac{2}{15} + 8 \cdot \frac{1}{3600}$

Step 2.2.3

Cancel the common factor of $8$ .

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Step 2.2.3.1

Factor $8$ out of $3600$ .

$8 + \frac{2}{15} + 8 \cdot \frac{1}{8 (450)}$

Step 2.2.3.2

Cancel the common factor.

$8 + \frac{2}{15} + 8 \cdot \frac{1}{8 \cdot 450}$

Step 2.2.3.3

Rewrite the expression.

$8 + \frac{2}{15} + \frac{1}{450}$

Step 2.3

Find the common denominator.

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Step 2.3.1

Write $8$ as a fraction with denominator $1$ .

$\frac{8}{1} + \frac{2}{15} + \frac{1}{450}$

Step 2.3.2

Multiply $\frac{8}{1}$ by $\frac{450}{450}$ .

$\frac{8}{1} \cdot \frac{450}{450} + \frac{2}{15} + \frac{1}{450}$

Step 2.3.3

Multiply $\frac{8}{1}$ by $\frac{450}{450}$ .

$\frac{8 \cdot 450}{450} + \frac{2}{15} + \frac{1}{450}$

Step 2.3.4

Multiply $\frac{2}{15}$ by $\frac{30}{30}$ .

$\frac{8 \cdot 450}{450} + \frac{2}{15} \cdot \frac{30}{30} + \frac{1}{450}$

Step 2.3.5

Multiply $\frac{2}{15}$ by $\frac{30}{30}$ .

$\frac{8 \cdot 450}{450} + \frac{2 \cdot 30}{15 \cdot 30} + \frac{1}{450}$

Step 2.3.6

Multiply $15$ by $30$ .

$\frac{8 \cdot 450}{450} + \frac{2 \cdot 30}{450} + \frac{1}{450}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{8 \cdot 450 + 2 \cdot 30 + 1}{450}$

Step 2.5

Simplify each term.

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Step 2.5.1

Multiply $8$ by $450$ .

$\frac{3600 + 2 \cdot 30 + 1}{450}$

Step 2.5.2

Multiply $2$ by $30$ .

$\frac{3600 + 60 + 1}{450}$

Step 2.6

Simplify by adding numbers.

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Step 2.6.1

Add $3600$ and $60$ .

$\frac{3660 + 1}{450}$

Step 2.6.2

Add $3660$ and $1$ .

$\frac{3661}{450}$

Step 3

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

$8.13\overline{5} °$