Basic Math Examples

$45$ , $1 \cdot 10^{- 5}$

Step 1

Multiply $10^{- 5}$ by $1$ .

$45, 10^{- 5}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$45, \frac{1}{10^{5}}$

Step 3

Raise $10$ to the power of $5$ .

$45, \frac{1}{100000}$

Step 4

The mean of a set of numbers is the sum divided by the number of terms.

$\frac{45 + \frac{1}{100000}}{2}$

Step 5

Simplify the numerator.

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Step 5.1

To write $45$ as a fraction with a common denominator, multiply by $\frac{100000}{100000}$ .

$\frac{45 \cdot \frac{100000}{100000} + \frac{1}{100000}}{2}$

Step 5.2

Combine $45$ and $\frac{100000}{100000}$ .

$\frac{\frac{45 \cdot 100000}{100000} + \frac{1}{100000}}{2}$

Step 5.3

Combine the numerators over the common denominator.

$\frac{\frac{45 \cdot 100000 + 1}{100000}}{2}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Multiply $45$ by $100000$ .

$\frac{\frac{4500000 + 1}{100000}}{2}$

Step 5.4.2

Add $4500000$ and $1$ .

$\frac{\frac{4500001}{100000}}{2}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{4500001}{100000} \cdot \frac{1}{2}$

Step 7

Multiply $\frac{4500001}{100000} \cdot \frac{1}{2}$ .

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Step 7.1

Multiply $\frac{4500001}{100000}$ by $\frac{1}{2}$ .

$\frac{4500001}{100000 \cdot 2}$

Step 7.2

Multiply $100000$ by $2$ .

$\frac{4500001}{200000}$

Step 8

Divide.

$22.500005$

Step 9

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$22.5$