Pre-Algebra Examples

$654000 \cdot 0.0001$

Step 1

Multiply $1$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 2

Multiply $1$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 3

Multiply $1$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 4

Multiply $1$ by $4$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 5

Multiply $1$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 6

Multiply $1$ by $6$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 7

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 8

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 9

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 10

Multiply $0$ by $4$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 11

Multiply $0$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 12

Multiply $0$ by $6$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 13

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 14

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 15

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 16

Multiply $0$ by $4$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 17

Multiply $0$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 18

Multiply $0$ by $6$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 19

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 20

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 21

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 22

Multiply $0$ by $4$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 23

Multiply $0$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 24

Multiply $0$ by $6$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 25

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 26

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 27

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 28

Multiply $0$ by $4$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 29

Multiply $0$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 30

Multiply $0$ by $6$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0001$ .


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

Step 31

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


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

Step 32

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


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

Step 33

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


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

Step 34

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


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

Step 35

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


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

Step 36

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


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

Step 37

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.

$65.4$