How to Multiply Two Decimals with Paper and Pencil

Nowadays, it seems as if everyone just punches numbers into a calculator and lets the calculator do all the work. What happens, though, when that calculator is nowhere to be found or doesn't work? You are left with having to get out a pencil and some paper and work the problem out by hand. So it is important to know how to do math problems by hand. Multiplying decimals is not much different from multiplying numbers without decimals. Both types of problems involve multiplying the bottom digits by all the top digits. When a decimal point is in one or both of the numbers being multiplied, then the answer must include a decimal point.

Instructions

1. Write down the problem by lining up the numbers. You don’t need to line up the decimal points, just the numbers. For example, if the problem is 3.8 x 6.24, you would line up the numbers by writing 3.8 on top and 6.24 on the bottom, or vice versa. Lining up the numbers means that the 4 would be under the 8, the 2 under the decimal point, the decimal point under the 3, and then the 6 not under anything.

2. Multiply as you would any other multiplication problem, ignoring the decimal points for now. For this example, begin by multiplying 4 x 8 = 32. Write down the 2 and carry the 3.

3. Multiply the 4 x 3 = 12 plus the 3 that was carried to result in 15. Write down the 15.

4. Write down a zero as a placeholder under the 152.

5. Multiply 2 x 8 = 16. Write down the 6 and carry the 1.

6. Multiply 2 x 3 = 6 plus the 1 that was carried to equal 7. Write down the 7.

7. Write down two zeroes this time as placeholders under the 760.

8. Multiply 6 x 8 = 48. Write down the 8 and carry the 4.

9. Multiply the 6 x 3 = 18 plus the 4 that was carried to give 22. Write down the 22.

10. Add to get the final answer. Add 152 + 760 + 22800 = 23712.

11. Determine where the decimal point goes. To do this, count the number of decimal places of the two numbers that were multiplied together, and put that number of decimal places in the answer. For this problem, 3.8 has one decimal place, and 6.24 has two decimal places. So three decimal places are involved. Starting from the right, count over three places to the left and put in the decimal point to give the final answer of 23.712.

Tips & Warnings

• Line up the numbers, not the decimal points.

• Put the decimal point in your answer.