Basic Math Examples

$(20 \cdot 5 \cdot 1.5 \cdot 10^{- 6} + 13.8 \cdot 10^{- 6}) \cdot 10^{6}$

Step 1

Simplify each term.

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Step 1.1

Multiply $20$ by $5$ .

$(100 \cdot 1.5 \cdot 10^{- 6} + 13.8 \cdot 10^{- 6}) \cdot 10^{6}$

Step 1.2

Multiply $100$ by $1.5$ .

$(150 \cdot 10^{- 6} + 13.8 \cdot 10^{- 6}) \cdot 10^{6}$

Step 1.3

Move the decimal point in $150$ to the left by $2$ places and increase the power of $10^{- 6}$ by $2$ .

$(1.5 \cdot 10^{- 4} + 13.8 \cdot 10^{- 6}) \cdot 10^{6}$

Step 1.4

Move the decimal point in $13.8$ to the left by $1$ place and increase the power of $10^{- 6}$ by $1$ .

$(1.5 \cdot 10^{- 4} + 1.38 \cdot 10^{- 5}) \cdot 10^{6}$

Step 2

Move the decimal point in $1.38$ to the left by $1$ place and increase the power of $10^{- 5}$ by $1$ .

$(1.5 \cdot 10^{- 4} + 0.138 \cdot 10^{- 4}) \cdot 10^{6}$

Step 3

Factor $10^{- 4}$ out of $1.5 \cdot 10^{- 4} + 0.138 \cdot 10^{- 4}$ .

$(1.5 + 0.138) \cdot 10^{- 4} \cdot 10^{6}$

Step 4

Add $1.5$ and $0.138$ .

$1.638 \cdot 10^{- 4} \cdot 10^{6}$

Step 5

Multiply $10^{- 4}$ by $10^{6}$ by adding the exponents.

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Step 5.1

Move $10^{6}$ .

$1.638 \cdot (10^{6} \cdot 10^{- 4})$

Step 5.2

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

$1.638 \cdot 10^{6 - 4}$

Step 5.3

Subtract $4$ from $6$ .

$1.638 \cdot 10^{2}$

Step 6

The result can be shown in multiple forms.

Scientific Notation:

$1.638 \cdot 10^{2}$

Expanded Form:

$163.8$