Basic Math Examples

$- 0.09 = 27 \cdot (22.2 \cdot 10^{- 6}) \cdot (t - 28)$

Step 1

Rewrite the equation as $27 \cdot 22.2 \cdot 10^{- 6} \cdot (t - 28) = - 0.09$ .

$27 \cdot 22.2 \cdot 10^{- 6} \cdot (t - 28) = - 0.09$

Step 2

Simplify.

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Step 2.1

Move the decimal point in $22.2$ to the left by $1$ place and increase the power of $10^{- 6}$ by $1$ .

$27 \cdot 2.22 \cdot 10^{- 5} \cdot (t - 28) = - 0.09$

Step 2.2

Multiply $27$ by $2.22$ .

$59.94 \cdot 10^{- 5} \cdot (t - 28) = - 0.09$

Step 2.3

Move the decimal point in $59.94$ to the left by $1$ place and increase the power of $10^{- 5}$ by $1$ .

$5.994 \cdot 10^{- 4} \cdot (t - 28) = - 0.09$

Step 3

Divide each term in $5.994 \cdot 10^{- 4} \cdot (t - 28) = - 0.09$ by $5.994 \cdot 10^{- 4}$ and simplify.

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Step 3.1

Divide each term in $5.994 \cdot 10^{- 4} \cdot (t - 28) = - 0.09$ by $5.994 \cdot 10^{- 4}$ .

$\frac{5.994 \cdot 10^{- 4} \cdot (t - 28)}{5.994 \cdot 10^{- 4}} = \frac{- 0.09}{5.994 \cdot 10^{- 4}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5.994$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5.994 \cdot 10^{- 4} \cdot (t - 28)}{5.994 \cdot 10^{- 4}} = \frac{- 0.09}{5.994 \cdot 10^{- 4}}$

Step 3.2.1.2

Rewrite the expression.

$\frac{10^{- 4} \cdot (t - 28)}{10^{- 4}} = \frac{- 0.09}{5.994 \cdot 10^{- 4}}$

Step 3.2.2

Cancel the common factor of $10^{- 4}$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{10^{- 4} \cdot (t - 28)}{10^{- 4}} = \frac{- 0.09}{5.994 \cdot 10^{- 4}}$

Step 3.2.2.2

Divide $t - 28$ by $1$ .

$t - 28 = \frac{- 0.09}{5.994 \cdot 10^{- 4}}$

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.

$t - 28 = (\frac{- 0.09}{5.994}) (\frac{1}{10^{- 4}})$

Step 3.3.1.2

Divide $- 0.09$ by $5.994$ .

$t - 28 = - 0.\overline{015} \frac{1}{10^{- 4}}$

Step 3.3.1.3

Move $10^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$t - 28 = - 0.\overline{015} \cdot 10^{4}$

Step 3.3.2

Move the decimal point in $- 0.\overline{015}$ to the right by $2$ places and decrease the power of $10^{4}$ by $2$ .

$t - 28 = - 1.\overline{501} \cdot 10^{2}$

Step 4

Move all terms not containing $t$ to the right side of the equation.

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Step 4.1

Add $28$ to both sides of the equation.

$t = - 1.\overline{501} \cdot 10^{2} + 28$

Step 4.2

Convert $28$ to scientific notation.

$t = - 1.\overline{501} \cdot 10^{2} + 2.8 \cdot 10^{1}$

Step 4.3

Move the decimal point in $2.8$ to the left by $1$ place and increase the power of $10^{1}$ by $1$ .

$t = - 1.\overline{501} \cdot 10^{2} + 0.28 \cdot 10^{2}$

Step 4.4

Factor $10^{2}$ out of $- 1.\overline{501} \cdot 10^{2} + 0.28 \cdot 10^{2}$ .

$t = (- 1.\overline{501} + 0.28) \cdot 10^{2}$

Step 4.5

Add $- 1.\overline{501}$ and $0.28$ .

$t = - 1.22\overline{150} \cdot 10^{2}$

Step 5

The result can be shown in multiple forms.

Scientific Notation:

$t = - 1.22\overline{150} \cdot 10^{2}$

Expanded Form:

$t = - 122.\overline{150}$