Finite Math Examples

$\frac{(7.6432 \cdot 10^{7}) (4.45 \cdot 10^{- 8})}{1.36 \cdot 10^{3}}$

Step 1

Multiply $7.6432$ by $4.45$ .

$\frac{34.01224 (10^{7} \cdot 10^{- 8})}{1.36 \cdot 10^{3}}$

Step 2

Multiply $10^{7}$ by $10^{- 8}$ 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.

$\frac{34.01224 \cdot 10^{7 - 8}}{1.36 \cdot 10^{3}}$

Step 2.2

Subtract $8$ from $7$ .

$\frac{34.01224 \cdot 10^{- 1}}{1.36 \cdot 10^{3}}$

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.

$(\frac{34.01224}{1.36}) (\frac{10^{- 1}}{10^{3}})$

Step 3.2

Divide $34.01224$ by $1.36$ .

$25.009 \frac{10^{- 1}}{10^{3}}$

Step 3.3

Subtract the exponent from the denominator from the exponent of the numerator for the same base

$25.009 \cdot 10^{- 1 + 3 \cdot - 1}$

Step 3.4

Multiply $3$ by $- 1$ .

$25.009 \cdot 10^{- 1 - 3}$

Step 3.5

Subtract $3$ from $- 1$ .

$25.009 \cdot 10^{- 4}$

Step 4

Move the decimal point in $25.009$ to the left by $1$ place and increase the power of $10^{- 4}$ by $1$ .

$2.5009 \cdot 10^{- 3}$

Step 5

The result can be shown in multiple forms.

Scientific Notation:

$2.5009 \cdot 10^{- 3}$

Expanded Form:

$0.0025009$