Chemistry Examples

$81.35 \cdot 62.77$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply $7$ by $5$ . Place the ones digit $(5)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in $62.77$ .

			$3$
	$8$	$1$	. $3$	$5$
$⨯$	$6$	$2$	. $7$	$7$
				$5$

Step 1.2

Multiply $7$ by $3$ and add the carried $3$ . Place the ones digit $(4)$ in the result line and carry the tens digit $(2)$ . There is one result line for each digit in the $62.77$ .

		$2$	$3$
	$8$	$1$	. $3$	$5$
$⨯$	$6$	$2$	. $7$	$7$
			$4$	$5$

Step 1.3

Multiply $7$ by $1$ 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 $62.77$ .

		$2$	$3$
	$8$	$1$	. $3$	$5$
$⨯$	$6$	$2$	. $7$	$7$
		$9$	$4$	$5$

Step 1.4

Multiply $7$ by $8$ . Place the ones digit $(6)$ in the result line and carry the tens digit $(5)$ . There is one result line for each digit in $62.77$ .


	$8$	$1$	. $3$	$5$
$⨯$	$6$	$2$	. $7$	$7$
$5$	$6$	$9$	$4$	$5$

Step 1.5

Multiply $7$ by $5$ . Place the ones digit $(5)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in $62.77$ .

			$3$
	$8$	$1$	. $3$	$5$
$⨯$	$6$	$2$	. $7$	$7$
$5$	$6$	$9$	$4$	$5$
			$5$

Step 1.6

Multiply $7$ by $3$ and add the carried $3$ . Place the ones digit $(4)$ in the result line and carry the tens digit $(2)$ . There is one result line for each digit in the $62.77$ .

		$2$	$3$
	$8$	$1$	. $3$	$5$
$⨯$	$6$	$2$	. $7$	$7$
$5$	$6$	$9$	$4$	$5$
		$4$	$5$

Step 1.7

Multiply $7$ by $1$ 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 $62.77$ .

		$2$	$3$
	$8$	$1$	. $3$	$5$
$⨯$	$6$	$2$	. $7$	$7$
$5$	$6$	$9$	$4$	$5$
	$9$	$4$	$5$

Step 1.8

Multiply $7$ by $8$ . Place the ones digit $(6)$ in the result line and carry the tens digit $(5)$ . There is one result line for each digit in $62.77$ .


		$8$	$1$	. $3$	$5$
	$⨯$	$6$	$2$	. $7$	$7$
	$5$	$6$	$9$	$4$	$5$
$5$	$6$	$9$	$4$	$5$

Step 1.9

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 $62.77$ .

				$1$
		$8$	$1$	. $3$	$5$
	$⨯$	$6$	$2$	. $7$	$7$
	$5$	$6$	$9$	$4$	$5$
$5$	$6$	$9$	$4$	$5$
			$0$

Step 1.10

Multiply $2$ by $3$ 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 $62.77$ .

				$1$
		$8$	$1$	. $3$	$5$
	$⨯$	$6$	$2$	. $7$	$7$
	$5$	$6$	$9$	$4$	$5$
$5$	$6$	$9$	$4$	$5$
		$7$	$0$

Step 1.11

Multiply $2$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $62.77$ .

				$1$
		$8$	$1$	. $3$	$5$
	$⨯$	$6$	$2$	. $7$	$7$
	$5$	$6$	$9$	$4$	$5$
$5$	$6$	$9$	$4$	$5$
	$2$	$7$	$0$

Step 1.12

Multiply $2$ by $8$ . Place the ones digit $(6)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $62.77$ .


			$8$	$1$	. $3$	$5$
		$⨯$	$6$	$2$	. $7$	$7$
		$5$	$6$	$9$	$4$	$5$
	$5$	$6$	$9$	$4$	$5$
$1$	$6$	$2$	$7$	$0$

Step 1.13

Multiply $6$ by $5$ . Place the ones digit $(0)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in $62.77$ .

					$3$
			$8$	$1$	. $3$	$5$
		$⨯$	$6$	$2$	. $7$	$7$
		$5$	$6$	$9$	$4$	$5$
	$5$	$6$	$9$	$4$	$5$
$1$	$6$	$2$	$7$	$0$
			$0$

Step 1.14

Multiply $6$ by $3$ and add the carried $3$ . Place the ones digit $(1)$ in the result line and carry the tens digit $(2)$ . There is one result line for each digit in the $62.77$ .

				$2$	$3$
			$8$	$1$	. $3$	$5$
		$⨯$	$6$	$2$	. $7$	$7$
		$5$	$6$	$9$	$4$	$5$
	$5$	$6$	$9$	$4$	$5$
$1$	$6$	$2$	$7$	$0$
		$1$	$0$

Step 1.15

Multiply $6$ by $1$ 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 $62.77$ .

				$2$	$3$
			$8$	$1$	. $3$	$5$
		$⨯$	$6$	$2$	. $7$	$7$
		$5$	$6$	$9$	$4$	$5$
	$5$	$6$	$9$	$4$	$5$
$1$	$6$	$2$	$7$	$0$
	$8$	$1$	$0$

Step 1.16

Multiply $6$ by $8$ . Place the ones digit $(8)$ in the result line and carry the tens digit $(4)$ . There is one result line for each digit in $62.77$ .


				$8$	$1$	. $3$	$5$
			$⨯$	$6$	$2$	. $7$	$7$
			$5$	$6$	$9$	$4$	$5$
		$5$	$6$	$9$	$4$	$5$
	$1$	$6$	$2$	$7$	$0$
$4$	$8$	$8$	$1$	$0$

Step 1.17

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


				$8$	$1$	. $3$	$5$
			$⨯$	$6$	$2$	. $7$	$7$
			$5$	$6$	$9$	$4$	$5$
		$5$	$6$	$9$	$4$	$5$
	$1$	$6$	$2$	$7$	$0$
$4$	$8$	$8$	$1$	$0$
							$5$

Step 1.18

Add the numbers in each column. In this case, add $4 + 5 + 0 + 0$ , then place the $9$ in the result line.


				$8$	$1$	. $3$	$5$
			$⨯$	$6$	$2$	. $7$	$7$
			$5$	$6$	$9$	$4$	$5$
		$5$	$6$	$9$	$4$	$5$
	$1$	$6$	$2$	$7$	$0$
$4$	$8$	$8$	$1$	$0$
						$9$	$5$

Step 1.19

Add the numbers in each column. In this case, add $9 + 4 + 0 + 0$ , then place the $3$ in the result line and carry the $1$ .


				$8$	$1$	. $3$	$5$
			$⨯$	$6$	$2$	. $7$	$7$
			$5$	$6$	$9$	$4$	$5$
		$5$	$6$	$9$	$4$	$5$
	$1$	$6$	$2$	$7$	$0$
$4$	$8$	$8$	$1$	$0$
					$3$	$9$	$5$

Step 1.20

Add the numbers in each column. In this case, add $6 + 9 + 7 + 0 + 1$ , then place the $3$ in the result line and carry the $2$ .


				$8$	$1$	. $3$	$5$
			$⨯$	$6$	$2$	. $7$	$7$
			$5$	$6$	$9$	$4$	$5$
		$5$	$6$	$9$	$4$	$5$
	$1$	$6$	$2$	$7$	$0$
$4$	$8$	$8$	$1$	$0$
				$3$	$3$	$9$	$5$

Step 1.21

Add the numbers in each column. In this case, add $5 + 6 + 2 + 1 + 2$ , then place the $6$ in the result line and carry the $1$ .


				$8$	$1$	. $3$	$5$
			$⨯$	$6$	$2$	. $7$	$7$
			$5$	$6$	$9$	$4$	$5$
		$5$	$6$	$9$	$4$	$5$
	$1$	$6$	$2$	$7$	$0$
$4$	$8$	$8$	$1$	$0$
			$6$	$3$	$3$	$9$	$5$

Step 1.22

Add the numbers in each column. In this case, add $0 + 5 + 6 + 8 + 1$ , then place the $0$ in the result line and carry the $2$ .


				$8$	$1$	. $3$	$5$
			$⨯$	$6$	$2$	. $7$	$7$
			$5$	$6$	$9$	$4$	$5$
		$5$	$6$	$9$	$4$	$5$
	$1$	$6$	$2$	$7$	$0$
$4$	$8$	$8$	$1$	$0$
		$0$	$6$	$3$	$3$	$9$	$5$

Step 1.23

Add the numbers in each column. In this case, add $0 + 0 + 1 + 8 + 2$ , then place the $1$ in the result line and carry the $1$ .


				$8$	$1$	. $3$	$5$
			$⨯$	$6$	$2$	. $7$	$7$
			$5$	$6$	$9$	$4$	$5$
		$5$	$6$	$9$	$4$	$5$
	$1$	$6$	$2$	$7$	$0$
$4$	$8$	$8$	$1$	$0$
	$1$	$0$	$6$	$3$	$3$	$9$	$5$

Step 1.24

Add the numbers in each column. In this case, add $0 + 0 + 0 + 4 + 1$ , then place the $5$ in the result line.


				$8$	$1$	. $3$	$5$
			$⨯$	$6$	$2$	. $7$	$7$
			$5$	$6$	$9$	$4$	$5$
		$5$	$6$	$9$	$4$	$5$
	$1$	$6$	$2$	$7$	$0$
$4$	$8$	$8$	$1$	$0$
$5$	$1$	$0$	$6$	$3$	$3$	$9$	$5$


				$8$	$1$	. $3$	$5$
			$⨯$	$6$	$2$	. $7$	$7$
			$5$	$6$	$9$	$4$	$5$
		$5$	$6$	$9$	$4$	$5$
	$1$	$6$	$2$	$7$	$0$
$4$	$8$	$8$	$1$	$0$
$5$	$1$	$0$	$6$	$3$	$3$	$9$	$5$

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.

$5106.3395$