Pre-Algebra Examples

$1 \cdot 10^{3} + 8 \cdot 10^{2} + 2 \cdot 10 + 5 \cdot 10^{0} + 6 \cdot \frac{1}{10}$

Step 1

Move the decimal point in $8$ to the left by $1$ place and increase the power of $10^{2}$ by $1$ .

$1 \cdot 10^{3} + 0.8 \cdot 10^{3} + 2 \cdot 10 + 5 \cdot 10^{0} + 6 \cdot \frac{1}{10}$

Step 2

Factor $10^{3}$ out of $1 \cdot 10^{3} + 0.8 \cdot 10^{3}$ .

$(1 + 0.8) \cdot 10^{3} + 2 \cdot 10 + 5 \cdot 10^{0} + 6 \cdot \frac{1}{10}$

Step 3

Add $1$ and $0.8$ .

$1.8 \cdot 10^{3} + 2 \cdot 10 + 5 \cdot 10^{0} + 6 \cdot \frac{1}{10}$

Step 4

Raise $10$ to the power of $1$ .

$1.8 \cdot 10^{3} + 2 \cdot 10^{1} + 5 \cdot 10^{0} + 6 \cdot \frac{1}{10}$

Step 5

Move the decimal point in $2$ to the left by $2$ places and increase the power of $10^{1}$ by $2$ .

$1.8 \cdot 10^{3} + 0.02 \cdot 10^{3} + 5 \cdot 10^{0} + 6 \cdot \frac{1}{10}$

Step 6

Factor $10^{3}$ out of $1.8 \cdot 10^{3} + 0.02 \cdot 10^{3}$ .

$(1.8 + 0.02) \cdot 10^{3} + 5 \cdot 10^{0} + 6 \cdot \frac{1}{10}$

Step 7

Add $1.8$ and $0.02$ .

$1.82 \cdot 10^{3} + 5 \cdot 10^{0} + 6 \cdot \frac{1}{10}$

Step 8

Move the decimal point in $5$ to the left by $3$ places and increase the power of $10^{0}$ by $3$ .

$1.82 \cdot 10^{3} + 0.005 \cdot 10^{3} + 6 \cdot \frac{1}{10}$

Step 9

Simplify with factoring out.

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Step 9.1

Factor $10^{3}$ out of $1.82 \cdot 10^{3} + 0.005 \cdot 10^{3}$ .

$(1.82 + 0.005) \cdot 10^{3} + 6 \cdot \frac{1}{10}$

Step 9.2

Add $1.82$ and $0.005$ .

$1.825 \cdot 10^{3} + 6 \cdot \frac{1}{10}$

Step 10

Simplify each term.

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Step 10.1

Cancel the common factor of $2$ .

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Step 10.1.1

Factor $2$ out of $6$ .

$1.825 \cdot 10^{3} + 2 (3) \cdot \frac{1}{10}$

Step 10.1.2

Factor $2$ out of $10$ .

$1.825 \cdot 10^{3} + 2 \cdot 3 \cdot \frac{1}{2 \cdot 5}$

Step 10.1.3

Cancel the common factor.

$1.825 \cdot 10^{3} + 2 \cdot 3 \cdot \frac{1}{2 \cdot 5}$

Step 10.1.4

Rewrite the expression.

$1.825 \cdot 10^{3} + 3 \cdot \frac{1}{5}$

Step 10.2

Combine $3$ and $\frac{1}{5}$ .

$1.825 \cdot 10^{3} + \frac{3}{5}$

Step 11

To write $1.825 \cdot 10^{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$1.825 \cdot 10^{3} \cdot \frac{5}{5} + \frac{3}{5}$

Step 12

Combine $1.825 \cdot 10^{3}$ and $\frac{5}{5}$ .

$\frac{1.825 \cdot 10^{3} \cdot 5}{5} + \frac{3}{5}$

Step 13

Combine the numerators over the common denominator.

$\frac{1.825 \cdot 10^{3} \cdot 5 + 3}{5}$

Step 14

Simplify the numerator.

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Step 14.1

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

$\frac{1.825 \cdot 1000 \cdot 5 + 3}{5}$

Step 14.2

Multiply $1.825$ by $1000$ .

$\frac{1825 \cdot 5 + 3}{5}$

Step 14.3

Multiply $1825$ by $5$ .

$\frac{9125 + 3}{5}$

Step 14.4

Add $9125$ and $3$ .

$\frac{9128}{5}$

Step 15

Cancel the common factor of $9128$ and $5$ .

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Step 15.1

Rewrite $9128$ as $1 (9128)$ .

$\frac{1 (9128)}{5}$

Step 15.2

Cancel the common factors.

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Step 15.2.1

Rewrite $5$ as $1 (5)$ .

$\frac{1 \cdot 9128}{1 \cdot 5}$

Step 15.2.2

Cancel the common factor.

$\frac{1 \cdot 9128}{1 \cdot 5}$

Step 15.2.3

Rewrite the expression.

$\frac{9128}{5}$

Step 16

The result can be shown in multiple forms.

Exact Form:

$\frac{9128}{5}$

Decimal Form:

$1825.6$

Mixed Number Form:

$1825 \frac{3}{5}$