Precalculus Examples

$165 ° 37' 44''$

Step 1

Since $165$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $37$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $44$ by $\frac{1}{3600}$ . Add them together.

$165 + 37 \cdot \frac{1}{60} + 44 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$165 + 37 \cdot \frac{1}{60} + 44 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Combine $37$ and $\frac{1}{60}$ .

$165 + \frac{37}{60} + 44 \cdot \frac{1}{3600}$

Step 2.2.2

Cancel the common factor of $4$ .

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Step 2.2.2.1

Factor $4$ out of $44$ .

$165 + \frac{37}{60} + 4 (11) \cdot \frac{1}{3600}$

Step 2.2.2.2

Factor $4$ out of $3600$ .

$165 + \frac{37}{60} + 4 \cdot 11 \cdot \frac{1}{4 \cdot 900}$

Step 2.2.2.3

Cancel the common factor.

$165 + \frac{37}{60} + 4 \cdot 11 \cdot \frac{1}{4 \cdot 900}$

Step 2.2.2.4

Rewrite the expression.

$165 + \frac{37}{60} + 11 \cdot \frac{1}{900}$

Step 2.2.3

Combine $11$ and $\frac{1}{900}$ .

$165 + \frac{37}{60} + \frac{11}{900}$

Step 2.3

Find the common denominator.

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Step 2.3.1

Write $165$ as a fraction with denominator $1$ .

$\frac{165}{1} + \frac{37}{60} + \frac{11}{900}$

Step 2.3.2

Multiply $\frac{165}{1}$ by $\frac{900}{900}$ .

$\frac{165}{1} \cdot \frac{900}{900} + \frac{37}{60} + \frac{11}{900}$

Step 2.3.3

Multiply $\frac{165}{1}$ by $\frac{900}{900}$ .

$\frac{165 \cdot 900}{900} + \frac{37}{60} + \frac{11}{900}$

Step 2.3.4

Multiply $\frac{37}{60}$ by $\frac{15}{15}$ .

$\frac{165 \cdot 900}{900} + \frac{37}{60} \cdot \frac{15}{15} + \frac{11}{900}$

Step 2.3.5

Multiply $\frac{37}{60}$ by $\frac{15}{15}$ .

$\frac{165 \cdot 900}{900} + \frac{37 \cdot 15}{60 \cdot 15} + \frac{11}{900}$

Step 2.3.6

Reorder the factors of $60 \cdot 15$ .

$\frac{165 \cdot 900}{900} + \frac{37 \cdot 15}{15 \cdot 60} + \frac{11}{900}$

Step 2.3.7

Multiply $15$ by $60$ .

$\frac{165 \cdot 900}{900} + \frac{37 \cdot 15}{900} + \frac{11}{900}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{165 \cdot 900 + 37 \cdot 15 + 11}{900}$

Step 2.5

Simplify each term.

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Step 2.5.1

Multiply $165$ by $900$ .

$\frac{148500 + 37 \cdot 15 + 11}{900}$

Step 2.5.2

Multiply $37$ by $15$ .

$\frac{148500 + 555 + 11}{900}$

Step 2.6

Reduce the expression by cancelling the common factors.

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Step 2.6.1

Add $148500$ and $555$ .

$\frac{149055 + 11}{900}$

Step 2.6.2

Add $149055$ and $11$ .

$\frac{149066}{900}$

Step 2.6.3

Cancel the common factor of $149066$ and $900$ .

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Step 2.6.3.1

Factor $2$ out of $149066$ .

$\frac{2 (74533)}{900}$

Step 2.6.3.2

Cancel the common factors.

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Step 2.6.3.2.1

Factor $2$ out of $900$ .

$\frac{2 \cdot 74533}{2 \cdot 450}$

Step 2.6.3.2.2

Cancel the common factor.

$\frac{2 \cdot 74533}{2 \cdot 450}$

Step 2.6.3.2.3

Rewrite the expression.

$\frac{74533}{450}$

Step 3

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

$165.62\overline{8} °$