Basic Math Examples

$\frac{(1.96 \cdot 10^{8}) (3.51 \cdot 10^{- 1})}{(4 \cdot 10^{4}) (3 \cdot 10^{7})}$

Step 1

Multiply $1.96$ by $3.51$ .

$\frac{6.8796 (10^{8} \cdot 10^{- 1})}{(4 \cdot 10^{4}) (3 \cdot 10^{7})}$

Step 2

Multiply $10^{8}$ by $10^{- 1}$ 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.

$\frac{6.8796 \cdot 10^{8 - 1}}{(4 \cdot 10^{4}) (3 \cdot 10^{7})}$

Step 2.2

Subtract $1$ from $8$ .

$\frac{6.8796 \cdot 10^{7}}{(4 \cdot 10^{4}) (3 \cdot 10^{7})}$

Step 3

Multiply $4$ by $3$ .

$\frac{6.8796 \cdot 10^{7}}{12 (10^{4} \cdot 10^{7})}$

Step 4

Multiply $10^{4}$ by $10^{7}$ by adding the exponents.

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Step 4.1

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

$\frac{6.8796 \cdot 10^{7}}{12 \cdot 10^{4 + 7}}$

Step 4.2

Add $4$ and $7$ .

$\frac{6.8796 \cdot 10^{7}}{12 \cdot 10^{11}}$

Step 5

Divide using scientific notation.

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Step 5.1

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

$(\frac{6.8796}{12}) (\frac{10^{7}}{10^{11}})$

Step 5.2

Divide $6.8796$ by $12$ .

$0.5733 \frac{10^{7}}{10^{11}}$

Step 5.3

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

$0.5733 \cdot 10^{7 + 11 \cdot - 1}$

Step 5.4

Multiply $11$ by $- 1$ .

$0.5733 \cdot 10^{7 - 11}$

Step 5.5

Subtract $11$ from $7$ .

$0.5733 \cdot 10^{- 4}$

Step 6

Move the decimal point in $0.5733$ to the right by $1$ place and decrease the power of $10^{- 4}$ by $1$ .

$5.733 \cdot 10^{- 5}$