Trigonometry Examples

$25 \cdot 3.14$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply $4$ by $5$ . Place the ones digit $(0)$ in the result line and carry the tens digit $(2)$ . There is one result line for each digit in $3.14$ .

		$2$
		$2$	$5$
$⨯$	$3$	. $1$	$4$
			$0$

Step 1.2

Multiply $4$ by $2$ and add the carried $2$ . Place the ones digit $(0)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in the $3.14$ .


		$2$	$5$
$⨯$	$3$	. $1$	$4$
	$1$	$0$	$0$

Step 1.3

Multiply $1$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $3.14$ .


		$2$	$5$
$⨯$	$3$	. $1$	$4$
	$1$	$0$	$0$
		$5$

Step 1.4

Multiply $1$ by $2$ . Place the result in the next column in the result line. There is one result line for each digit in $3.14$ .


		$2$	$5$
$⨯$	$3$	. $1$	$4$
	$1$	$0$	$0$
	$2$	$5$

Step 1.5

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 $3.14$ .

		$1$
		$2$	$5$
$⨯$	$3$	. $1$	$4$
	$1$	$0$	$0$
	$2$	$5$
	$5$

Step 1.6

Multiply $3$ by $2$ 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 $3.14$ .


		$2$	$5$
$⨯$	$3$	. $1$	$4$
	$1$	$0$	$0$
	$2$	$5$
$7$	$5$

Step 1.7

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


		$2$	$5$
$⨯$	$3$	. $1$	$4$
	$1$	$0$	$0$
	$2$	$5$
$7$	$5$
			$0$

Step 1.8

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


		$2$	$5$
$⨯$	$3$	. $1$	$4$
	$1$	$0$	$0$
	$2$	$5$
$7$	$5$
		$5$	$0$

Step 1.9

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


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

Step 1.10

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


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


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

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.

$78.5$