Basic Math Examples

$3.2 \times 10^{- 19} \cdot 750 \times 10^{3} \cdot 0.01 \cdot \sin (45)$

Step 1

Multiply $10^{- 19}$ by $10^{3}$ by adding the exponents.

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Step 1.1

Move $10^{3}$ .

$3.2 \cdot (10^{3} \cdot 10^{- 19}) \cdot 750 \cdot 0.01 \cdot \sin (45)$

Step 1.2

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

$3.2 \cdot 10^{3 - 19} \cdot 750 \cdot 0.01 \cdot \sin (45)$

Step 1.3

Subtract $19$ from $3$ .

$3.2 \cdot 10^{- 16} \cdot 750 \cdot 0.01 \cdot \sin (45)$

Step 2

Multiply $3.2$ by $750$ .

$2400 \cdot 10^{- 16} \cdot 0.01 \cdot \sin (45)$

Step 3

Multiply $2400$ by $0.01$ .

$24 \cdot 10^{- 16} \cdot \sin (45)$

Step 4

Move the decimal point in $24$ to the left by $1$ place and increase the power of $10^{- 16}$ by $1$ .

$2.4 \cdot 10^{- 15} \cdot \sin (45)$

Step 5

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$2.4 \cdot 10^{- 15} \cdot \frac{\sqrt{2}}{2}$

Step 6

Multiply $2.4 \cdot 10^{- 15} \frac{\sqrt{2}}{2}$ .

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Step 6.1

Combine $2.4$ and $\frac{\sqrt{2}}{2}$ .

$10^{- 15} \frac{2.4 \sqrt{2}}{2}$

Step 6.2

Multiply $2.4$ by $\sqrt{2}$ .

$10^{- 15} \frac{3.39411254}{2}$

Step 6.3

Combine $10^{- 15}$ and $\frac{3.39411254}{2}$ .

$\frac{10^{- 15} \cdot 3.39411254}{2}$

Step 7

Move $10^{- 15}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3.39411254}{2 \cdot 10^{15}}$

Step 8

Divide using scientific notation.

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Step 8.1

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

$(\frac{3.39411254}{2}) (\frac{1}{10^{15}})$

Step 8.2

Divide $3.39411254$ by $2$ .

$1.69705627 \frac{1}{10^{15}}$

Step 8.3

Move $10^{15}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$1.69705627 \cdot 10^{- 15}$