Stacking multiplications 6 - decimals

We have learned how to stack to calculate, for example, 36 times 2. We stack like this, we calculate … and arrive at 36 times 2 equals 72. But what if we instead … … have a decimal in one of the numbers? 3.6 times 2? Well, we stack the same way as before.

The number with the most digits goes on top, that is 3.6. The two goes in the next row. Then we calculate the same way as before, without caring about the decimal point. Yes, at this stage, we pretend it is not there. 2 times 6 is 12.

We get a memory digit of 1, and write 2 here. 2 times 3 is 6. Plus the memory digit 1. This is 7, which we write here. So we have 7 and 2 below the bar.

But this is not the product we are looking for. There is one more thing to do: We will count how many decimals there are in the factors. One decimal, right? This means it should be one decimal in the product too. Now we are done: 3,6 times 2 equals 7,2.

And we have learned that we can multiply decimal numbers by stacking them. It’s very similar to how we calculate with factors without decimals. The difference is that we count how many decimals the factors have altogether, and then we place the decimal point in the right spot. Let’s look at another example to better learn how it works. 2,13 times 2,3.

Two numbers which both contain decimals. Let’s start with the stacking. The number with the most digits, 2,13, goes on top. As you can see, one decimal point is diagonally above the other, and this may well be the case. It’s no problem.

Now we calculate, digit by digit, as if the decimal points were not there: 3 times 3 is 9. 3 times 1 is 3. And 3 times 2 is 6. Next, the digit on the lower row. 2 times 3 is 6.

2 times 1 is 2. 2 times 2 is 4. We keep calculating as if the decimal point was not there. So we need to sum it up, like before 9 … 3 + 6 is 9 … 6 + 2 is 8 … And 4. And now we need to do one more thing.

Remember? We will count how many decimals there are altogether in the factors. One, two, three. And then we will count to three decimals in the product too. One, two, three - we place the decimal point there.

And 2,13 times 2,3 equals 4,899.