The Lesson

Long multiplication is a method for multiplying numbers. Long multiplication can be used for numbers with digits after the decimal point. The long multiplication below shows what we mean by using a number with digits after the decimal point:

In this long multiplication, 1.4 has a digit (4) after a decimal point (.).

A Real Example of How to Do Long Multiplication with Decimals

Doing long multiplication with decimals is easy.

Question

Multiply the numbers below.

Step-by-Step:

1

Write the numbers you wish to multiply, one underneath the other.
The trick with long multiplication with decimals is to ignore the decimal point at first and do a long multiplication as normal.

2

Find the right most digit of the bottom number (in the units column).

3

Find the right most digit of the top number (in the units column).

4

Multiply the bottom digit (4) with the top digit (5).
5 × 4 = 20

5

Check if the answer from Step 4 is 9 or less: No. 20 is not 9 or less.
  • If No, the answer will have two digits.
  • Write the digit on the right underneath the column (beneath the line).
  • Carry the left digit to the column to the left.

6

Move a digit to the left in the top number.

7

  • Multiply the bottom digit (4) with the top digit (2).
    2 × 4 = 8
  • Add any carried numbers to the answer.
    8 + 2 = 10

8

Check if the answer from Step 7 is 9 or less: No. 10 is not 9 or less.
  • If No, the answer will have two digits.
  • Write the digit on the right underneath the column (beneath the line).
  • Carry the left digit to the column to the left.

9

Move a digit to the left in the top number. There are no more digits to the left.

10

Write the carried digit underneath the line.

11

Write a 0 on the right in a new row underneath the line.

12

Move a digit to the left in the bottom number (in the tens column).

13

Find the right most digit of the top number (in the units column).

14

Multiply the bottom digit (1) with the top digit (5).
5 × 1 = 5

15

Check if the answer from Step 4 is 9 or less: Yes. 5 is 9 or less.
  • If Yes, write the number beneath the line, to the left of the 0.

16

Move a digit to the left in the top number.

17

Multiply the bottom digit (1) with the top digit (2).
2 × 1 = 2

18

Check if the answer from Step 17 is 9 or less: Yes. 2 is 9 or less.
  • If Yes, write the number below beneath the line.

19

Move a digit to the left in the top number. There are no more digits to the left.

20

Use long addition to add the two numbers beneath the line.
We have completed the long multiplication having ignored the decimal point. Now we consider the decimal point again.

21

Count the number of digits after the decimal point. There is 1 digit after the decimal point (a 4).

22

Ensure there are as many digits after the decimal point (1) in the answer (350). There is 1 digit after the decimal point (a 4).

Answer:

The solution to 25 × 1.4 is 35.

Lesson Slides

The slider below shows another real example of how to do long multiplication with decimals.

Parts of an Multiplication

  • The numbers you multiply together are factors.
  • The result of multiplying the numbers is the product.