Chemistry Examples

$788.1 \cdot 8.1$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply $1$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $8.1$ .


	$7$	$8$	$8$	. $1$
$⨯$			$8$	. $1$
				$1$

Step 1.2

Multiply $1$ by $8$ . Place the result in the next column in the result line. There is one result line for each digit in $8.1$ .


	$7$	$8$	$8$	. $1$
$⨯$			$8$	. $1$
			$8$	$1$

Step 1.3

Multiply $1$ by $8$ . Place the result in the next column in the result line. There is one result line for each digit in $8.1$ .


	$7$	$8$	$8$	. $1$
$⨯$			$8$	. $1$
		$8$	$8$	$1$

Step 1.4

Multiply $1$ by $7$ . Place the result in the next column in the result line. There is one result line for each digit in $8.1$ .


	$7$	$8$	$8$	. $1$
$⨯$			$8$	. $1$
	$7$	$8$	$8$	$1$

Step 1.5

Multiply $8$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $8.1$ .


	$7$	$8$	$8$	. $1$
$⨯$			$8$	. $1$
	$7$	$8$	$8$	$1$
			$8$

Step 1.6

Multiply $8$ by $8$ . Place the ones digit $(4)$ in the result line and carry the tens digit $(6)$ . There is one result line for each digit in $8.1$ .

		$6$
	$7$	$8$	$8$	. $1$
$⨯$			$8$	. $1$
	$7$	$8$	$8$	$1$
		$4$	$8$

Step 1.7

Multiply $8$ by $8$ and add the carried $6$ . Place the ones digit $(0)$ in the result line and carry the tens digit $(7)$ . There is one result line for each digit in the $8.1$ .

	$7$	$6$
	$7$	$8$	$8$	. $1$
$⨯$			$8$	. $1$
	$7$	$8$	$8$	$1$
	$0$	$4$	$8$

Step 1.8

Multiply $8$ by $7$ and add the carried $7$ . Place the ones digit $(3)$ in the result line and carry the tens digit $(6)$ . There is one result line for each digit in the $8.1$ .


		$7$	$8$	$8$	. $1$
	$⨯$			$8$	. $1$
		$7$	$8$	$8$	$1$
$6$	$3$	$0$	$4$	$8$

Step 1.9

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


		$7$	$8$	$8$	. $1$
	$⨯$			$8$	. $1$
		$7$	$8$	$8$	$1$
$6$	$3$	$0$	$4$	$8$
					$1$

Step 1.10

Add the numbers in each column. In this case, add $8 + 8$ , then place the $6$ in the result line and carry the $1$ .


		$7$	$8$	$8$	. $1$
	$⨯$			$8$	. $1$
		$7$	$8$	$8$	$1$
$6$	$3$	$0$	$4$	$8$
				$6$	$1$

Step 1.11

Add the numbers in each column. In this case, add $8 + 4 + 1$ , then place the $3$ in the result line and carry the $1$ .


		$7$	$8$	$8$	. $1$
	$⨯$			$8$	. $1$
		$7$	$8$	$8$	$1$
$6$	$3$	$0$	$4$	$8$
			$3$	$6$	$1$

Step 1.12

Add the numbers in each column. In this case, add $7 + 0 + 1$ , then place the $8$ in the result line.


		$7$	$8$	$8$	. $1$
	$⨯$			$8$	. $1$
		$7$	$8$	$8$	$1$
$6$	$3$	$0$	$4$	$8$
		$8$	$3$	$6$	$1$

Step 1.13

Add the numbers in each column. In this case, add $0 + 3$ , then place the $3$ in the result line.


		$7$	$8$	$8$	. $1$
	$⨯$			$8$	. $1$
		$7$	$8$	$8$	$1$
$6$	$3$	$0$	$4$	$8$
	$3$	$8$	$3$	$6$	$1$

Step 1.14

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


		$7$	$8$	$8$	. $1$
	$⨯$			$8$	. $1$
		$7$	$8$	$8$	$1$
$6$	$3$	$0$	$4$	$8$
$6$	$3$	$8$	$3$	$6$	$1$


		$7$	$8$	$8$	. $1$
	$⨯$			$8$	. $1$
		$7$	$8$	$8$	$1$
$6$	$3$	$0$	$4$	$8$
$6$	$3$	$8$	$3$	$6$	$1$

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.

$6383.61$