Long Multiplication

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

See also

Long Addition
Long Subtraction
Long decimal Division
Long Euclidean Division
Big numbers Calculator
Number Calculators
Mathematics Calculators

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