Basic Math Examples

$10^{- 3} + 10^{- 2} + 10 + 10^{- 1} + 10^{- 2}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$\frac{1}{10^{3}} + 10^{- 2} + 10 + 10^{- 1} + 10^{- 2}$

Step 1.2

Raise $10$ to the power of $3$ .

$\frac{1}{1000} + 10^{- 2} + 10 + 10^{- 1} + 10^{- 2}$

Step 1.3

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

$\frac{1}{1000} + \frac{1}{10^{2}} + 10 + 10^{- 1} + 10^{- 2}$

Step 1.4

Raise $10$ to the power of $2$ .

$\frac{1}{1000} + \frac{1}{100} + 10 + 10^{- 1} + 10^{- 2}$

Step 1.5

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

$\frac{1}{1000} + \frac{1}{100} + 10 + \frac{1}{10} + 10^{- 2}$

Step 1.6

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

$\frac{1}{1000} + \frac{1}{100} + 10 + \frac{1}{10} + \frac{1}{10^{2}}$

Step 1.7

Raise $10$ to the power of $2$ .

$\frac{1}{1000} + \frac{1}{100} + 10 + \frac{1}{10} + \frac{1}{100}$

Step 2

Combine fractions.

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

$10 + \frac{1}{1000} + \frac{1 + 1}{100} + \frac{1}{10}$

Step 2.2

Add $1$ and $1$ .

$10 + \frac{1}{1000} + \frac{2}{100} + \frac{1}{10}$

Step 3

Find the common denominator.

Tap for more steps...

Step 3.1

Write $10$ as a fraction with denominator $1$ .

$\frac{10}{1} + \frac{1}{1000} + \frac{2}{100} + \frac{1}{10}$

Step 3.2

Multiply $\frac{10}{1}$ by $\frac{1000}{1000}$ .

$\frac{10}{1} \cdot \frac{1000}{1000} + \frac{1}{1000} + \frac{2}{100} + \frac{1}{10}$

Step 3.3

Multiply $\frac{10}{1}$ by $\frac{1000}{1000}$ .

$\frac{10 \cdot 1000}{1000} + \frac{1}{1000} + \frac{2}{100} + \frac{1}{10}$

Step 3.4

Multiply $\frac{2}{100}$ by $\frac{10}{10}$ .

$\frac{10 \cdot 1000}{1000} + \frac{1}{1000} + \frac{2}{100} \cdot \frac{10}{10} + \frac{1}{10}$

Step 3.5

Multiply $\frac{2}{100}$ by $\frac{10}{10}$ .

$\frac{10 \cdot 1000}{1000} + \frac{1}{1000} + \frac{2 \cdot 10}{100 \cdot 10} + \frac{1}{10}$

Step 3.6

Multiply $\frac{1}{10}$ by $\frac{100}{100}$ .

$\frac{10 \cdot 1000}{1000} + \frac{1}{1000} + \frac{2 \cdot 10}{100 \cdot 10} + \frac{1}{10} \cdot \frac{100}{100}$

Step 3.7

Multiply $\frac{1}{10}$ by $\frac{100}{100}$ .

$\frac{10 \cdot 1000}{1000} + \frac{1}{1000} + \frac{2 \cdot 10}{100 \cdot 10} + \frac{100}{10 \cdot 100}$

Step 3.8

Reorder the factors of $100 \cdot 10$ .

$\frac{10 \cdot 1000}{1000} + \frac{1}{1000} + \frac{2 \cdot 10}{10 \cdot 100} + \frac{100}{10 \cdot 100}$

Step 3.9

Multiply $10$ by $100$ .

$\frac{10 \cdot 1000}{1000} + \frac{1}{1000} + \frac{2 \cdot 10}{1000} + \frac{100}{10 \cdot 100}$

Step 3.10

Multiply $10$ by $100$ .

$\frac{10 \cdot 1000}{1000} + \frac{1}{1000} + \frac{2 \cdot 10}{1000} + \frac{100}{1000}$

Step 4

Combine the numerators over the common denominator.

$\frac{10 \cdot 1000 + 1 + 2 \cdot 10 + 100}{1000}$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Multiply $10$ by $1000$ .

$\frac{10000 + 1 + 2 \cdot 10 + 100}{1000}$

Step 5.2

Multiply $2$ by $10$ .

$\frac{10000 + 1 + 20 + 100}{1000}$

Step 6

Simplify by adding numbers.

Tap for more steps...

Step 6.1

Add $10000$ and $1$ .

$\frac{10001 + 20 + 100}{1000}$

Step 6.2

Add $10001$ and $20$ .

$\frac{10021 + 100}{1000}$

Step 6.3

Add $10021$ and $100$ .

$\frac{10121}{1000}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{10121}{1000}$

Decimal Form:

$10.121$

Mixed Number Form:

$10 \frac{121}{1000}$