Basic Math Examples

$3.14 {(\frac{d}{2})}^{2} = \frac{57 \cdot 9.8}{2.1 \cdot 10^{8}}$

Step 1

Simplify.

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Step 1.1

Multiply $57$ by $9.8$ .

$3.14 {(\frac{d}{2})}^{2} = \frac{558.6}{2.1 \cdot 10^{8}}$

Step 1.2

Divide using scientific notation.

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Step 1.2.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$3.14 {(\frac{d}{2})}^{2} = (\frac{558.6}{2.1}) (\frac{1}{10^{8}})$

Step 1.2.2

Divide $558.6$ by $2.1$ .

$3.14 {(\frac{d}{2})}^{2} = 266 \frac{1}{10^{8}}$

Step 1.2.3

Move $10^{8}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3.14 {(\frac{d}{2})}^{2} = 266 \cdot 10^{- 8}$

Step 1.3

Move the decimal point in $266$ to the left by $2$ places and increase the power of $10^{- 8}$ by $2$ .

$3.14 {(\frac{d}{2})}^{2} = 2.66 \cdot 10^{- 6}$

Step 2

Divide each term in $3.14 {(\frac{d}{2})}^{2} = 2.66 \cdot 10^{- 6}$ by $3.14$ and simplify.

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Step 2.1

Divide each term in $3.14 {(\frac{d}{2})}^{2} = 2.66 \cdot 10^{- 6}$ by $3.14$ .

$\frac{3.14 {(\frac{d}{2})}^{2}}{3.14} = \frac{2.66 \cdot 10^{- 6}}{3.14}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3.14$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3.14 {(\frac{d}{2})}^{2}}{3.14} = \frac{2.66 \cdot 10^{- 6}}{3.14}$

Step 2.2.1.2

Divide ${(\frac{d}{2})}^{2}$ by $1$ .

${(\frac{d}{2})}^{2} = \frac{2.66 \cdot 10^{- 6}}{3.14}$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Apply the product rule to $\frac{d}{2}$ .

$\frac{d^{2}}{2^{2}} = \frac{2.66 \cdot 10^{- 6}}{3.14}$

Step 2.2.2.2

Raise $2$ to the power of $2$ .

$\frac{d^{2}}{4} = \frac{2.66 \cdot 10^{- 6}}{3.14}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide using scientific notation.

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Step 2.3.1.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$\frac{d^{2}}{4} = (\frac{2.66}{3.14}) (\frac{10^{- 6}}{1})$

Step 2.3.1.2

Divide $2.66$ by $3.14$ .

$\frac{d^{2}}{4} = 0.84713375 \frac{10^{- 6}}{1}$

Step 2.3.1.3

Divide $10^{- 6}$ by $1$ .

$\frac{d^{2}}{4} = 0.84713375 \cdot 10^{- 6}$

Step 2.3.2

Move the decimal point in $0.84713375$ to the right by $1$ place and decrease the power of $10^{- 6}$ by $1$ .

$\frac{d^{2}}{4} = 8.47133757 \cdot 10^{- 7}$

Step 3

Multiply both sides of the equation by $4$ .

$4 \frac{d^{2}}{4} = 4 \cdot 8.47133757 \cdot 10^{- 7}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1

Cancel the common factor.

$4 \frac{d^{2}}{4} = 4 \cdot 8.47133757 \cdot 10^{- 7}$

Step 4.1.1.2

Rewrite the expression.

$d^{2} = 4 \cdot 8.47133757 \cdot 10^{- 7}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $4 \cdot 8.47133757 \cdot 10^{- 7}$ .

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Step 4.2.1.1

Multiply $4$ by $8.47133757$ .

$d^{2} = 33.88535031 \cdot 10^{- 7}$

Step 4.2.1.2

Move the decimal point in $33.88535031$ to the left by $1$ place and increase the power of $10^{- 7}$ by $1$ .

$d^{2} = 3.38853503 \cdot 10^{- 6}$

Step 5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$d = \pm \sqrt{3.38853503 \cdot 10^{- 6}}$

Step 6

Simplify $\pm \sqrt{3.38853503 \cdot 10^{- 6}}$ .

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Step 6.1

Rewrite $\sqrt{3.38853503 \cdot 10^{- 6}}$ as $\sqrt{3.38853503} \cdot \sqrt{10^{- 6}}$ .

$d = \pm \sqrt{3.38853503} \cdot \sqrt{10^{- 6}}$

Step 6.2

Evaluate the root.

$d = \pm 1.84079739 \cdot \sqrt{10^{- 6}}$

Step 6.3

Rewrite $10^{- 6}$ as ${(10^{- 3})}^{2}$ .

$d = \pm 1.84079739 \cdot \sqrt{{(10^{- 3})}^{2}}$

Step 6.4

Pull terms out from under the radical, assuming positive real numbers.

$d = \pm 1.84079739 \cdot 10^{- 3}$

Step 7

The complete solution is the result of both the positive and negative portions of the solution.

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Step 7.1

First, use the positive value of the $\pm$ to find the first solution.

$d = 1.84079739 \cdot 10^{- 3}$

Step 7.2

Next, use the negative value of the $\pm$ to find the second solution.

$d = - 1.84079739 \cdot 10^{- 3}$

Step 7.3

The complete solution is the result of both the positive and negative portions of the solution.

$d = 1.84079739 \cdot 10^{- 3}, - 1.84079739 \cdot 10^{- 3}$

Step 8

The result can be shown in multiple forms.

Scientific Notation:

$d = 1.84079739 \cdot 10^{- 3}, - 1.84079739 \cdot 10^{- 3}$

Expanded Form:

$d = 0.00184079, - 0.00184079$