Basic Math Examples

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

Step 1

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

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

Step 2

Simplify.

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Step 2.1

Multiply $25$ by $22.2$ .

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

Step 2.2

Remove parentheses.

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

Step 3

Divide each term in $555 \cdot 10^{- 6} (t - 19) = - 0.09$ by $5.55 \cdot 10^{- 4}$ and simplify.

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Step 3.1

Divide each term in $555 \cdot 10^{- 6} (t - 19) = - 0.09$ by $5.55 \cdot 10^{- 4}$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Move $10^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3.2.2

Multiply $10^{- 4}$ by $10^{6}$ by adding the exponents.

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Step 3.2.2.1

Move $10^{6}$ .

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

Step 3.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.2.2.3

Subtract $4$ from $6$ .

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

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.

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

Step 3.3.1.2

Divide $- 0.09$ by $5.55$ .

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

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:

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