Pre-Algebra Examples

$0.005 \cdot 0.0021$

Step 1

Multiply $1$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .


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

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 $0.0021$ .


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

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 $0.0021$ .


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

Step 4

Multiply $1$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .


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

Step 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 $0.0021$ .

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

Step 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 $0.0021$ .

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

Step 7

Multiply $2$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .

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

Step 8

Multiply $2$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .


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

Step 9

Multiply $0$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .


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

Step 10

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .


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

Step 11

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .


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

Step 12

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .


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

Step 13

Multiply $0$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .


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

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 $0.0021$ .


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

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 $0.0021$ .


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

Step 16

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .


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

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 $0.0021$ .


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

Step 18

Multiply $0$ by $0$ . Place the result in the next column in the result line. There is one result line for each digit in $0.0021$ .


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

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 $0.0021$ .


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

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 $0.0021$ .


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

Step 21

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


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

Step 22

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


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

Step 23

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


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

Step 24

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


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

Step 25

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


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

Step 26

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 $7$ , so the answer must have $7$ decimal places as well.

$0.0000105$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$