Basic Math Examples

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

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

Step 1

Simplify.

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Step 1.1

Multiply

57

$57$ by

9.8

$9.8$ .

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

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

Step 1.2.2

Divide

558.6

$558.6$ by

2.1

$2.1$ .

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

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

Step 1.2.3

Move

10^{8}

$10^{8}$ to the numerator using the negative exponent rule

\frac{1}{b^{n}} = b^{- n}

$\frac{1}{b^{n}} = b^{- n}$ .

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

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

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

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

Step 1.3

Move the decimal point in

266

$266$ to the left by

2

$2$ places and increase the power of

10^{- 8}

$10^{- 8}$ by

2

$2$ .

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

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

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

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

Step 2

Divide each term in

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

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

3.14

$3.14$ and simplify.

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Step 2.1

Divide each term in

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

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

3.14

$3.14$ .

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

$3.14$ .

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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:

$d = 0.00184079, - 0.00184079$