Basic Math Examples

- 0.09 = (25) (22.2 \cdot 10^{- 6}) (t - 19)

$- 0.09 = (25) (22.2 \cdot 10^{- 6}) (t - 19)$

Step 1

Rewrite the equation as

25 \cdot 22.2 \cdot (10^{- 6} (t - 19)) = - 0.09

$25 \cdot 22.2 \cdot (10^{- 6} (t - 19)) = - 0.09$ .

25 \cdot 22.2 \cdot (10^{- 6} (t - 19)) = - 0.09

$25 \cdot 22.2 \cdot (10^{- 6} (t - 19)) = - 0.09$

Step 2

Simplify.

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Step 2.1

Multiply

25

$25$ by

22.2

$22.2$ .

555 \cdot (10^{- 6} (t - 19)) = - 0.09

$555 \cdot (10^{- 6} (t - 19)) = - 0.09$

Step 2.2

Remove parentheses.

555 \cdot 10^{- 6} (t - 19) = - 0.09

$555 \cdot 10^{- 6} (t - 19) = - 0.09$

555 \cdot 10^{- 6} (t - 19) = - 0.09

$555 \cdot 10^{- 6} (t - 19) = - 0.09$

Step 3

Divide each term in

555 \cdot 10^{- 6} (t - 19) = - 0.09

$555 \cdot 10^{- 6} (t - 19) = - 0.09$ by

5.55 \cdot 10^{- 4}

$5.55 \cdot 10^{- 4}$ and simplify.

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Step 3.1

Divide each term in

555 \cdot 10^{- 6} (t - 19) = - 0.09

$555 \cdot 10^{- 6} (t - 19) = - 0.09$ by

5.55 \cdot 10^{- 4}

$5.55 \cdot 10^{- 4}$ .

\frac{555 \cdot 10^{- 6} (t - 19)}{5.55 \cdot 10^{- 4}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}

$\frac{555 \cdot 10^{- 6} (t - 19)}{5.55 \cdot 10^{- 4}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Move

10^{- 6}

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

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

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

\frac{555 (t - 19)}{5.55 \cdot 10^{- 4} \cdot 10^{6}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}

$\frac{555 (t - 19)}{5.55 \cdot 10^{- 4} \cdot 10^{6}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}$

Step 3.2.2

Multiply

10^{- 4}

$10^{- 4}$ by

10^{6}

$10^{6}$ by adding the exponents.

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Step 3.2.2.1

Move

10^{6}

$10^{6}$ .

\frac{555 (t - 19)}{5.55 \cdot (10^{6} \cdot 10^{- 4})} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}

$\frac{555 (t - 19)}{5.55 \cdot (10^{6} \cdot 10^{- 4})} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}$

Step 3.2.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{555 (t - 19)}{5.55 \cdot 10^{6 - 4}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}

$\frac{555 (t - 19)}{5.55 \cdot 10^{6 - 4}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}$

Step 3.2.2.3

Subtract

4

$4$ from

6

$6$ .

\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}

$\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}$

\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}

$\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}$

\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}

$\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = \frac{- 0.09}{5.55 \cdot 10^{- 4}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide using scientific notation.

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Step 3.3.1.1

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

\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = (\frac{- 0.09}{5.55}) (\frac{1}{10^{- 4}})

$\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = (\frac{- 0.09}{5.55}) (\frac{1}{10^{- 4}})$

Step 3.3.1.2

Divide

- 0.09

$- 0.09$ by

5.55

$5.55$ .

$\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = - 0.0\overline{162} \frac{1}{10^{- 4}}$

Step 3.3.1.3

Move

$10^{- 4}$ to the numerator using the negative exponent rule

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

$\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = - 0.0\overline{162} \cdot 10^{4}$

Step 3.3.2

Move the decimal point in

$- 0.0\overline{162}$ to the right by

$2$ places and decrease the power of

$10^{4}$ by

$2$ .

$\frac{555 (t - 19)}{5.55 \cdot 10^{2}} = - 1.\overline{621} \cdot 10^{2}$

Step 4

Multiply both sides of the equation by

$\frac{5.55 \cdot 10^{2}}{555}$ .

$\frac{5.55 \cdot 10^{2}}{555} \cdot \frac{555 (t - 19)}{5.55 \cdot 10^{2}} = \frac{5.55 \cdot 10^{2}}{555} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify

$\frac{5.55 \cdot 10^{2}}{555} \cdot \frac{555 (t - 19)}{5.55 \cdot 10^{2}}$ .

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Step 5.1.1.1

Divide using scientific notation.

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Step 5.1.1.1.1

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

$(\frac{5.55}{555}) (\frac{10^{2}}{1}) \frac{555 (t - 19)}{5.55 \cdot 10^{2}} = \frac{5.55 \cdot 10^{2}}{555} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.1.1.1.2

Divide

$5.55$ by

$555$ .

$0.01 \frac{10^{2}}{1} \frac{555 (t - 19)}{5.55 \cdot 10^{2}} = \frac{5.55 \cdot 10^{2}}{555} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.1.1.1.3

Divide

$10^{2}$ by

$1$ .

$0.01 \cdot 10^{2} \frac{555 (t - 19)}{5.55 \cdot 10^{2}} = \frac{5.55 \cdot 10^{2}}{555} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.1.1.2

Cancel the common factor of

$0.01 \cdot 10^{2}$ .

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Step 5.1.1.2.1

Factor

$0.01 \cdot 10^{2}$ out of

$5.55 \cdot 10^{2}$ .

$0.01 \cdot 10^{2} \frac{555 (t - 19)}{0.01 \cdot 10^{2} (555)} = \frac{5.55 \cdot 10^{2}}{555} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.1.1.2.2

Cancel the common factor.

$0.01 \cdot 10^{2} \frac{555 (t - 19)}{0.01 \cdot 10^{2} \cdot 555} = \frac{5.55 \cdot 10^{2}}{555} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.1.1.2.3

Rewrite the expression.

$\frac{555 (t - 19)}{555} = \frac{5.55 \cdot 10^{2}}{555} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.1.1.3

Cancel the common factor of

$555$ .

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Step 5.1.1.3.1

Cancel the common factor.

$\frac{555 (t - 19)}{555} = \frac{5.55 \cdot 10^{2}}{555} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.1.1.3.2

Divide

$t - 19$ by

$1$ .

$t - 19 = \frac{5.55 \cdot 10^{2}}{555} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify

$\frac{5.55 \cdot 10^{2}}{555} \cdot - 1.\overline{621} \cdot 10^{2}$ .

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Step 5.2.1.1

Divide using scientific notation.

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Step 5.2.1.1.1

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

$t - 19 = (\frac{5.55}{555}) (\frac{10^{2}}{1}) \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.2.1.1.2

Divide

$5.55$ by

$555$ .

$t - 19 = 0.01 \frac{10^{2}}{1} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.2.1.1.3

Divide

$10^{2}$ by

$1$ .

$t - 19 = 0.01 \cdot 10^{2} \cdot - 1.\overline{621} \cdot 10^{2}$

Step 5.2.1.2

Multiply

$0.01$ by

$- 1.\overline{621}$ .

$t - 19 = - 0.0\overline{162} (10^{2} \cdot 10^{2})$

Step 5.2.1.3

Multiply

$10^{2}$ by

$10^{2}$ by adding the exponents.

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Step 5.2.1.3.1

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t - 19 = - 0.0\overline{162} \cdot 10^{2 + 2}$

Step 5.2.1.3.2

Add

$2$ and

$2$ .

$t - 19 = - 0.0\overline{162} \cdot 10^{4}$

Step 5.2.1.4

Move the decimal point in

$- 0.0\overline{162}$ to the right by

$2$ places and decrease the power of

$10^{4}$ by

$2$ .

$t - 19 = - 1.\overline{621} \cdot 10^{2}$

Step 6

Move all terms not containing

$t$ to the right side of the equation.

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Step 6.1

Add

$19$ to both sides of the equation.

$t = - 1.\overline{621} \cdot 10^{2} + 19$

Step 6.2

Convert

$19$ to scientific notation.

$t = - 1.\overline{621} \cdot 10^{2} + 1.9 \cdot 10^{1}$

Step 6.3

Move the decimal point in

$1.9$ to the left by

$1$ place and increase the power of

$10^{1}$ by

$1$ .

$t = - 1.\overline{621} \cdot 10^{2} + 0.19 \cdot 10^{2}$

Step 6.4

Factor

$10^{2}$ out of

$- 1.\overline{621} \cdot 10^{2} + 0.19 \cdot 10^{2}$ .

$t = (- 1.\overline{621} + 0.19) \cdot 10^{2}$

Step 6.5

Add

$- 1.\overline{621}$ and

$0.19$ .

$t = - 1.43\overline{162} \cdot 10^{2}$

Step 7

The result can be shown in multiple forms.

Scientific Notation:

$t = - 1.43\overline{162} \cdot 10^{2}$

Expanded Form:

$t = - 143.\overline{162}$