# Long Multiplication

This tool performs the long multiplication of two (whole or decimal) numbers. Input two numbers one in each line.
input 2 numbers (one per line)

## Long Multiplication with Whole Numbers

We show in steps how to multiply two whole numbers using this example 565 x 893.

• Start by stacking the two numbers and aligning them to the right.

 5 6 5 × 8 9 3 =

• Multiply each digit of the second number by the first number starting from the first column (ones column) and put the result.

565 × 3 = 1695

Details are here : multiply 565 × 3 with carry

 5 6 5 × 8 9 3 1 6 9 5

• We proceed the same with the others digits of the second number.

565 × 9 = 5085 that we put in a row shifted by one digit to the left.

565 × 8 = 4520 in the same way, put in a new row shifted by one digit to the left.

We obtain,

 5 6 5 × 8 9 3 1 6 9 5 5 0 8 5 4 5 2 0

• Sum the three intermediate results to obtain,

 5 6 5 × 8 9 3 1 6 9 5 + 5 0 8 5 + 4 5 2 0 = 5 0 4 5 4 5

## Long Multiplication with decimal numbers

We multiply step by step two decimal numbers 654.521 × 76.43

• Count the total number of decimals in the two numbers.

654.521 has 3 decimals
76.43 has 2 decimals

That is a total of 3+2=5 decimals

• Multiply the two numbers after temporarily ignoring the decimal dots 654521 × 7643
To do so, follow the steps above to multiply whole numbers. We get,

 6 5 4 5 2 1 × 7 6 4 3 1 9 6 3 5 6 3 détails + 2 6 1 8 0 8 4 détails + 3 9 2 7 1 2 6 détails + 4 5 8 1 6 4 7 détails = 5 0 0 2 5 0 4 0 0 3

• We put the decimal dots ignored in the previous step by applying the following rule. The result has a number of decimals equal to the sum of the number of initial numbers decimals.

Here, the result must have 5 decimal digits. The final result is 50025.04003