Finite Math Examples

$\frac{3 \cdot 10^{2} \cdot 5 \cdot 10^{4}}{12 \cdot {(10^{3})}^{3}}$

Step 1

Multiply $3$ by $5$ .

$\frac{15 (10^{2} \cdot 10^{4})}{12 \cdot {(10^{3})}^{3}}$

Step 2

Multiply $10^{2}$ by $10^{4}$ by adding the exponents.

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Step 2.1

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

$\frac{15 \cdot 10^{2 + 4}}{12 \cdot {(10^{3})}^{3}}$

Step 2.2

Add $2$ and $4$ .

$\frac{15 \cdot 10^{6}}{12 \cdot {(10^{3})}^{3}}$

Step 3

Cancel the common factor of $15$ and $12$ .

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Step 3.1

Factor $3$ out of $15 \cdot 10^{6}$ .

$\frac{3 \cdot 5 \cdot 10^{6}}{12 \cdot {(10^{3})}^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $12 \cdot {(10^{3})}^{3}$ .

$\frac{3 \cdot 5 \cdot 10^{6}}{3 (4 \cdot {(10^{3})}^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{3 \cdot 5 \cdot 10^{6}}{3 (4 \cdot {(10^{3})}^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{5 \cdot 10^{6}}{4 \cdot {(10^{3})}^{3}}$

Step 4

Simplify the denominator.

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Step 4.1

Multiply the exponents in ${(10^{3})}^{3}$ .

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Step 4.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{5 \cdot 10^{6}}{4 \cdot 10^{3 \cdot 3}}$

Step 4.1.2

Multiply $3$ by $3$ .

$\frac{5 \cdot 10^{6}}{4 \cdot 10^{9}}$

Step 4.2

Raise $10$ to the power of $9$ .

$\frac{5 \cdot 10^{6}}{4 \cdot 1000000000}$

Step 5

Multiply $4$ by $1000000000$ .

$\frac{5 \cdot 10^{6}}{4000000000}$

Step 6

Divide using scientific notation.

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Step 6.1

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

$(\frac{5}{4000000000}) (\frac{10^{6}}{1})$

Step 6.2

Divide $5$ by $4000000000$ .

$0 \frac{10^{6}}{1}$

Step 6.3

Divide $10^{6}$ by $1$ .

$0 \cdot 10^{6}$

Step 7

Move the decimal point in $0$ to the right by $9$ places and decrease the power of $10^{6}$ by $9$ .

$1.25 \cdot 10^{- 3}$

Step 8

The result can be shown in multiple forms.

Scientific Notation:

$1.25 \cdot 10^{- 3}$

Expanded Form:

$0.00125$