Chemistry Examples

$15.06 \cdot 11.03$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply $3$ by $6$ . Place the ones digit $(8)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $11.03$ .

			$1$
	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
				$8$

Step 1.2

Multiply $3$ 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 $11.03$ .

			$1$
	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
			$1$	$8$

Step 1.3

Multiply $3$ by $5$ . Place the ones digit $(5)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $11.03$ .

	$1$		$1$
	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
		$5$	$1$	$8$

Step 1.4

Multiply $3$ by $1$ 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 $11.03$ .


	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
	$4$	$5$	$1$	$8$

Step 1.5

Multiply $0$ by $6$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
	$4$	$5$	$1$	$8$
			$0$

Step 1.6

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
	$4$	$5$	$1$	$8$
		$0$	$0$

Step 1.7

Multiply $0$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
	$4$	$5$	$1$	$8$
	$0$	$0$	$0$

Step 1.8

Multiply $0$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
	$4$	$5$	$1$	$8$
$0$	$0$	$0$	$0$

Step 1.9

Multiply $1$ by $6$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
	$4$	$5$	$1$	$8$
$0$	$0$	$0$	$0$
		$6$

Step 1.10

Multiply $1$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
	$4$	$5$	$1$	$8$
$0$	$0$	$0$	$0$
	$0$	$6$

Step 1.11

Multiply $1$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


	$1$	$5$	. $0$	$6$
$⨯$	$1$	$1$	. $0$	$3$
	$4$	$5$	$1$	$8$
$0$	$0$	$0$	$0$
$5$	$0$	$6$

Step 1.12

Multiply $1$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


		$1$	$5$	. $0$	$6$
	$⨯$	$1$	$1$	. $0$	$3$
		$4$	$5$	$1$	$8$
	$0$	$0$	$0$	$0$
$1$	$5$	$0$	$6$

Step 1.13

Multiply $1$ by $6$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


		$1$	$5$	. $0$	$6$
	$⨯$	$1$	$1$	. $0$	$3$
		$4$	$5$	$1$	$8$
	$0$	$0$	$0$	$0$
$1$	$5$	$0$	$6$
		$6$

Step 1.14

Multiply $1$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


		$1$	$5$	. $0$	$6$
	$⨯$	$1$	$1$	. $0$	$3$
		$4$	$5$	$1$	$8$
	$0$	$0$	$0$	$0$
$1$	$5$	$0$	$6$
	$0$	$6$

Step 1.15

Multiply $1$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


		$1$	$5$	. $0$	$6$
	$⨯$	$1$	$1$	. $0$	$3$
		$4$	$5$	$1$	$8$
	$0$	$0$	$0$	$0$
$1$	$5$	$0$	$6$
$5$	$0$	$6$

Step 1.16

Multiply $1$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $11.03$ .


			$1$	$5$	. $0$	$6$
		$⨯$	$1$	$1$	. $0$	$3$
			$4$	$5$	$1$	$8$
		$0$	$0$	$0$	$0$
	$1$	$5$	$0$	$6$
$1$	$5$	$0$	$6$

Step 1.17

Add the numbers in each column. In this case, add $8 + 0 + 0 + 0$ , then place the $8$ in the result line.


			$1$	$5$	. $0$	$6$
		$⨯$	$1$	$1$	. $0$	$3$
			$4$	$5$	$1$	$8$
		$0$	$0$	$0$	$0$
	$1$	$5$	$0$	$6$
$1$	$5$	$0$	$6$
						$8$

Step 1.18

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


			$1$	$5$	. $0$	$6$
		$⨯$	$1$	$1$	. $0$	$3$
			$4$	$5$	$1$	$8$
		$0$	$0$	$0$	$0$
	$1$	$5$	$0$	$6$
$1$	$5$	$0$	$6$
					$1$	$8$

Step 1.19

Add the numbers in each column. In this case, add $5 + 0 + 6 + 0$ , then place the $1$ in the result line and carry the $1$ .


			$1$	$5$	. $0$	$6$
		$⨯$	$1$	$1$	. $0$	$3$
			$4$	$5$	$1$	$8$
		$0$	$0$	$0$	$0$
	$1$	$5$	$0$	$6$
$1$	$5$	$0$	$6$
				$1$	$1$	$8$

Step 1.20

Add the numbers in each column. In this case, add $4 + 0 + 0 + 6 + 1$ , then place the $1$ in the result line and carry the $1$ .


			$1$	$5$	. $0$	$6$
		$⨯$	$1$	$1$	. $0$	$3$
			$4$	$5$	$1$	$8$
		$0$	$0$	$0$	$0$
	$1$	$5$	$0$	$6$
$1$	$5$	$0$	$6$
			$1$	$1$	$1$	$8$

Step 1.21

Add the numbers in each column. In this case, add $0 + 0 + 5 + 0 + 1$ , then place the $6$ in the result line.


			$1$	$5$	. $0$	$6$
		$⨯$	$1$	$1$	. $0$	$3$
			$4$	$5$	$1$	$8$
		$0$	$0$	$0$	$0$
	$1$	$5$	$0$	$6$
$1$	$5$	$0$	$6$
		$6$	$1$	$1$	$1$	$8$

Step 1.22

Add the numbers in each column. In this case, add $0 + 0 + 1 + 5$ , then place the $6$ in the result line.


			$1$	$5$	. $0$	$6$
		$⨯$	$1$	$1$	. $0$	$3$
			$4$	$5$	$1$	$8$
		$0$	$0$	$0$	$0$
	$1$	$5$	$0$	$6$
$1$	$5$	$0$	$6$
	$6$	$6$	$1$	$1$	$1$	$8$

Step 1.23

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


			$1$	$5$	. $0$	$6$
		$⨯$	$1$	$1$	. $0$	$3$
			$4$	$5$	$1$	$8$
		$0$	$0$	$0$	$0$
	$1$	$5$	$0$	$6$
$1$	$5$	$0$	$6$
$1$	$6$	$6$	$1$	$1$	$1$	$8$


			$1$	$5$	. $0$	$6$
		$⨯$	$1$	$1$	. $0$	$3$
			$4$	$5$	$1$	$8$
		$0$	$0$	$0$	$0$
	$1$	$5$	$0$	$6$
$1$	$5$	$0$	$6$
$1$	$6$	$6$	$1$	$1$	$1$	$8$

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 $4$ , so the answer must have $4$ decimal places as well.

$166.1118$