Basic Math Examples

$\frac{(5.7 \cdot 10^{- 5}) \cdot 140}{(1.9 \cdot 10^{6}) \cdot (2.1 \cdot 10^{5})}$

Step 1

Multiply $5.7$ by $140$ .

$\frac{798 \cdot 10^{- 5}}{(1.9 \cdot 10^{6}) \cdot (2.1 \cdot 10^{5})}$

Step 2

Multiply $1.9$ by $2.1$ .

$\frac{798 \cdot 10^{- 5}}{3.99 (10^{6} \cdot 10^{5})}$

Step 3

Multiply $10^{6}$ by $10^{5}$ by adding the exponents.

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Step 3.1

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

$\frac{798 \cdot 10^{- 5}}{3.99 \cdot 10^{6 + 5}}$

Step 3.2

Add $6$ and $5$ .

$\frac{798 \cdot 10^{- 5}}{3.99 \cdot 10^{11}}$

Step 4

Divide using scientific notation.

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Step 4.1

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

$(\frac{798}{3.99}) (\frac{10^{- 5}}{10^{11}})$

Step 4.2

Divide $798$ by $3.99$ .

$200 \frac{10^{- 5}}{10^{11}}$

Step 4.3

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

$200 \cdot 10^{- 5 + 11 \cdot - 1}$

Step 4.4

Multiply $11$ by $- 1$ .

$200 \cdot 10^{- 5 - 11}$

Step 4.5

Subtract $11$ from $- 5$ .

$200 \cdot 10^{- 16}$

Step 5

Move the decimal point in $200$ to the left by $2$ places and increase the power of $10^{- 16}$ by $2$ .

$2 \cdot 10^{- 14}$