Linear Algebra Examples

$\frac{1.8 \cdot 10}{8.9 \cdot 10^{- 4}}$

Step 1

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

$\frac{1.8 \cdot 10 \cdot 10^{4}}{8.9}$

Step 2

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

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Step 2.1

Move $10^{4}$ .

$\frac{1.8 \cdot (10^{4} \cdot 10)}{8.9}$

Step 2.2

Multiply $10^{4}$ by $10$ .

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Step 2.2.1

Raise $10$ to the power of $1$ .

$\frac{1.8 \cdot (10^{4} \cdot 10^{1})}{8.9}$

Step 2.2.2

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

$\frac{1.8 \cdot 10^{4 + 1}}{8.9}$

Step 2.3

Add $4$ and $1$ .

$\frac{1.8 \cdot 10^{5}}{8.9}$

Step 3

Divide using scientific notation.

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Step 3.1

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

$(\frac{1.8}{8.9}) (\frac{10^{5}}{1})$

Step 3.2

Divide $1.8$ by $8.9$ .

$0.20224719 \frac{10^{5}}{1}$

Step 3.3

Divide $10^{5}$ by $1$ .

$0.20224719 \cdot 10^{5}$

Step 4

Move the decimal point in $0.20224719$ to the right by $1$ place and decrease the power of $10^{5}$ by $1$ .

$2.02247191 \cdot 10^{4}$

Step 5

The result can be shown in multiple forms.

Scientific Notation:

$2.02247191 \cdot 10^{4}$

Expanded Form:

$20224.71910112$