Precalculus Examples

$\frac{2 π}{b} = 0.1$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$b, 1$

Step 1.2

The LCM of one and any expression is the expression.

$b$

Step 2

Multiply each term in $\frac{2 π}{b} = 0.1$ by $b$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2 π}{b} = 0.1$ by $b$ .

$\frac{2 π}{b} b = 0.1 b$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $b$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 π}{b} b = 0.1 b$

Step 2.2.1.2

Rewrite the expression.

$2 π = 0.1 b$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $0.1 b = 2 π$ .

$0.1 b = 2 π$

Step 3.2

Divide each term in $0.1 b = 2 π$ by $0.1$ and simplify.

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Step 3.2.1

Divide each term in $0.1 b = 2 π$ by $0.1$ .

$\frac{0.1 b}{0.1} = \frac{2 π}{0.1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $0.1$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{0.1 b}{0.1} = \frac{2 π}{0.1}$

Step 3.2.2.1.2

Divide $b$ by $1$ .

$b = \frac{2 π}{0.1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Replace $π$ with an approximation.

$b = \frac{2 \cdot 3.14159265}{0.1}$

Step 3.2.3.2

Multiply $2$ by $3.14159265$ .

$b = \frac{6.2831853}{0.1}$

Step 3.2.3.3

Divide $6.2831853$ by $0.1$ .

$b = 62.83185307$