# Long Multiplication

## 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

## See also

Long Addition

Long Subtraction

Long decimal Division

Long Euclidean Division

Big numbers Calculator

Number Calculators

Mathematics Calculators