Chemistry Examples

$0.5 \cdot 22.4$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply $4$ by $5$ . Place the ones digit $(0)$ in the result line and carry the tens digit $(2)$ . There is one result line for each digit in $22.4$ .

		$2$
		$0$	. $5$
$⨯$	$2$	$2$	. $4$
			$0$

Step 1.2

Multiply $4$ by $0$ and add the carried $2$ . Place the result in the next column in the result line. There is one result line for each digit in $22.4$ .


		$0$	. $5$
$⨯$	$2$	$2$	. $4$
		$2$	$0$

Step 1.3

Multiply $2$ by $5$ . Place the ones digit $(0)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $22.4$ .

		$1$
		$0$	. $5$
$⨯$	$2$	$2$	. $4$
		$2$	$0$
		$0$

Step 1.4

Multiply $2$ by $0$ and add the carried $1$ . Place the result in the next column in the result line. There is one result line for each digit in $22.4$ .


		$0$	. $5$
$⨯$	$2$	$2$	. $4$
		$2$	$0$
	$1$	$0$

Step 1.5

Multiply $2$ by $5$ . Place the ones digit $(0)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $22.4$ .

		$1$
		$0$	. $5$
$⨯$	$2$	$2$	. $4$
		$2$	$0$
	$1$	$0$
	$0$

Step 1.6

Multiply $2$ by $0$ and add the carried $1$ . Place the result in the next column in the result line. There is one result line for each digit in $22.4$ .


		$0$	. $5$
$⨯$	$2$	$2$	. $4$
		$2$	$0$
	$1$	$0$
$1$	$0$

Step 1.7

Add the numbers in each column. In this case, add $0 + 0 + 0$ , then place the $0$ in the result line.


		$0$	. $5$
$⨯$	$2$	$2$	. $4$
		$2$	$0$
	$1$	$0$
$1$	$0$
			$0$

Step 1.8

Add the numbers in each column. In this case, add $2 + 0 + 0$ , then place the $2$ in the result line.


		$0$	. $5$
$⨯$	$2$	$2$	. $4$
		$2$	$0$
	$1$	$0$
$1$	$0$
		$2$	$0$

Step 1.9

Add the numbers in each column. In this case, add $0 + 1 + 0$ , then place the $1$ in the result line.


		$0$	. $5$
$⨯$	$2$	$2$	. $4$
		$2$	$0$
	$1$	$0$
$1$	$0$
	$1$	$2$	$0$

Step 1.10

Add the numbers in each column. In this case, add $0 + 0 + 1$ , then place the $1$ in the result line.


		$0$	. $5$
$⨯$	$2$	$2$	. $4$
		$2$	$0$
	$1$	$0$
$1$	$0$
$1$	$1$	$2$	$0$


		$0$	. $5$
$⨯$	$2$	$2$	. $4$
		$2$	$0$
	$1$	$0$
$1$	$0$
$1$	$1$	$2$	$0$

Step 2

To find the number of decimal places needed in the answer, add the number of decimal places in the multiplier and multiplicand. In this case, there is a total of $2$ , so the answer must have $2$ decimal places as well.

$11.2$