Basic Math Examples

\frac{1}{1 + 5 \cdot \frac{256}{12 \cdot 10^{- 6}}}

$\frac{1}{1 + 5 \cdot \frac{256}{12 \cdot 10^{- 6}}}$

Step 1

Divide using scientific notation.

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Step 1.1

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

\frac{1}{1 + 5 \cdot ((\frac{256}{12}) (\frac{1}{10^{- 6}}))}

$\frac{1}{1 + 5 \cdot ((\frac{256}{12}) (\frac{1}{10^{- 6}}))}$

Step 1.2

Divide

256

$256$ by

12

$12$ .

\frac{1}{1 + 5 \cdot (21.\overline{3} \frac{1}{10^{- 6}})}

$\frac{1}{1 + 5 \cdot (21.\overline{3} \frac{1}{10^{- 6}})}$

Step 1.3

Move

10^{- 6}

$10^{- 6}$ to the numerator using the negative exponent rule

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

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

\frac{1}{1 + 5 \cdot 21.\overline{3} \cdot 10^{6}}

$\frac{1}{1 + 5 \cdot 21.\overline{3} \cdot 10^{6}}$

\frac{1}{1 + 5 \cdot 21.\overline{3} \cdot 10^{6}}

$\frac{1}{1 + 5 \cdot 21.\overline{3} \cdot 10^{6}}$

Step 2

Multiply

5

$5$ by

21.\overline{3}

$21.\overline{3}$ .

\frac{1}{1 + 106.\overline{6} \cdot 10^{6}}

$\frac{1}{1 + 106.\overline{6} \cdot 10^{6}}$

Step 3

Convert

1

$1$ to scientific notation.

\frac{1}{1 \cdot 10^{0} + 106.\overline{6} \cdot 10^{6}}

$\frac{1}{1 \cdot 10^{0} + 106.\overline{6} \cdot 10^{6}}$

Step 4

Move the decimal point in

1

$1$ to the left by

6

$6$ places and increase the power of

10^{0}

$10^{0}$ by

6

$6$ .

\frac{1}{0.000001 \cdot 10^{6} + 106.\overline{6} \cdot 10^{6}}

$\frac{1}{0.000001 \cdot 10^{6} + 106.\overline{6} \cdot 10^{6}}$

Step 5

Factor

10^{6}

$10^{6}$ out of

0.000001 \cdot 10^{6} + 106.\overline{6} \cdot 10^{6}

$0.000001 \cdot 10^{6} + 106.\overline{6} \cdot 10^{6}$ .

\frac{1}{(0.000001 + 106.\overline{6}) \cdot 10^{6}}

$\frac{1}{(0.000001 + 106.\overline{6}) \cdot 10^{6}}$

Step 6

Add

0.000001

$0.000001$ and

106.\overline{6}

$106.\overline{6}$ .

\frac{1}{106.666667\overline{6} \cdot 10^{6}}

$\frac{1}{106.666667\overline{6} \cdot 10^{6}}$

Step 7

Move the decimal point in

106.666667\overline{6}

$106.666667\overline{6}$ to the left by

2

$2$ places and increase the power of

10^{6}

$10^{6}$ by

2

$2$ .

\frac{1}{1.06666667 \cdot 10^{8}}

$\frac{1}{1.06666667 \cdot 10^{8}}$

Step 8

Divide using scientific notation.

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Step 8.1

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

(\frac{1}{1.06666667}) (\frac{1}{10^{8}})

$(\frac{1}{1.06666667}) (\frac{1}{10^{8}})$

Step 8.2

Divide

1

$1$ by

1.06666667

$1.06666667$ .

0.93749999 \frac{1}{10^{8}}

$0.93749999 \frac{1}{10^{8}}$

Step 8.3

Move

10^{8}

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

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

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

0.93749999 \cdot 10^{- 8}

$0.93749999 \cdot 10^{- 8}$

0.93749999 \cdot 10^{- 8}

$0.93749999 \cdot 10^{- 8}$

Step 9

Move the decimal point in

0.93749999

$0.93749999$ to the right by

1

$1$ place and decrease the power of

10^{- 8}

$10^{- 8}$ by

1

$1$ .

9.37499991 \cdot 10^{- 9}

$9.37499991 \cdot 10^{- 9}$