Precalculus Examples

$35 ° 58' 38''$

Step 1

Since $35$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $58$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $38$ by $\frac{1}{3600}$ . Add them together.

$35 + 58 \cdot \frac{1}{60} + 38 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$35 + 58 \cdot \frac{1}{60} + 38 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Factor $2$ out of $58$ .

$35 + 2 (29) \cdot \frac{1}{60} + 38 \cdot \frac{1}{3600}$

Step 2.2.1.2

Factor $2$ out of $60$ .

$35 + 2 \cdot 29 \cdot \frac{1}{2 \cdot 30} + 38 \cdot \frac{1}{3600}$

Step 2.2.1.3

Cancel the common factor.

$35 + 2 \cdot 29 \cdot \frac{1}{2 \cdot 30} + 38 \cdot \frac{1}{3600}$

Step 2.2.1.4

Rewrite the expression.

$35 + 29 \cdot \frac{1}{30} + 38 \cdot \frac{1}{3600}$

Step 2.2.2

Combine $29$ and $\frac{1}{30}$ .

$35 + \frac{29}{30} + 38 \cdot \frac{1}{3600}$

Step 2.2.3

Cancel the common factor of $2$ .

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Step 2.2.3.1

Factor $2$ out of $38$ .

$35 + \frac{29}{30} + 2 (19) \cdot \frac{1}{3600}$

Step 2.2.3.2

Factor $2$ out of $3600$ .

$35 + \frac{29}{30} + 2 \cdot 19 \cdot \frac{1}{2 \cdot 1800}$

Step 2.2.3.3

Cancel the common factor.

$35 + \frac{29}{30} + 2 \cdot 19 \cdot \frac{1}{2 \cdot 1800}$

Step 2.2.3.4

Rewrite the expression.

$35 + \frac{29}{30} + 19 \cdot \frac{1}{1800}$

Step 2.2.4

Combine $19$ and $\frac{1}{1800}$ .

$35 + \frac{29}{30} + \frac{19}{1800}$

Step 2.3

Find the common denominator.

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Step 2.3.1

Write $35$ as a fraction with denominator $1$ .

$\frac{35}{1} + \frac{29}{30} + \frac{19}{1800}$

Step 2.3.2

Multiply $\frac{35}{1}$ by $\frac{1800}{1800}$ .

$\frac{35}{1} \cdot \frac{1800}{1800} + \frac{29}{30} + \frac{19}{1800}$

Step 2.3.3

Multiply $\frac{35}{1}$ by $\frac{1800}{1800}$ .

$\frac{35 \cdot 1800}{1800} + \frac{29}{30} + \frac{19}{1800}$

Step 2.3.4

Multiply $\frac{29}{30}$ by $\frac{60}{60}$ .

$\frac{35 \cdot 1800}{1800} + \frac{29}{30} \cdot \frac{60}{60} + \frac{19}{1800}$

Step 2.3.5

Multiply $\frac{29}{30}$ by $\frac{60}{60}$ .

$\frac{35 \cdot 1800}{1800} + \frac{29 \cdot 60}{30 \cdot 60} + \frac{19}{1800}$

Step 2.3.6

Multiply $30$ by $60$ .

$\frac{35 \cdot 1800}{1800} + \frac{29 \cdot 60}{1800} + \frac{19}{1800}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{35 \cdot 1800 + 29 \cdot 60 + 19}{1800}$

Step 2.5

Simplify each term.

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Step 2.5.1

Multiply $35$ by $1800$ .

$\frac{63000 + 29 \cdot 60 + 19}{1800}$

Step 2.5.2

Multiply $29$ by $60$ .

$\frac{63000 + 1740 + 19}{1800}$

Step 2.6

Simplify by adding numbers.

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Step 2.6.1

Add $63000$ and $1740$ .

$\frac{64740 + 19}{1800}$

Step 2.6.2

Add $64740$ and $19$ .

$\frac{64759}{1800}$

Step 3

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

$35.977\overline{2} °$