Multiply Decimals

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How to correctly multiply decimals by hand

If you already know how to do long multiplication then multiplying decimals is a doddle. Simply follow these two steps:

1. Ignore the decimal points (for now) and do a regular long multiplication with the numbers.

For example, let's work out 5.6 * 8.4.

  56 <- Remove all decimals
  84
----
4704

2. Now we need to put the decimal point back into the answer. The number of decimal places that the answer will have is equal to how many decimals places (in total) were in the question.

For example, 5.6 and 8.4 have a combined total of 2 decimal numbers (6 and 4). Therefore the answer will have two decimals.

So, imagine that the answer is currently 4704.0. What we need to do is move the decimal point 2 places to the left, the answer then becomes 47.04 which is the correct final answer. This method of multiplying decimals works everytime no matter what numbers or how many you use.

Let's try a more complicated example, 0.0024 * 1.38 * 0.5:

  138 <- Ignore all decimal places and points
   24
    5
-----
16560

Again, we need to put the decimal point back into the answer. First, count how many decimals are in the original expression. 0024 + 38 + 5 = 7 decimal places.

Imagining that the answer is currently 16560.0, we move the point 7 places to the left. The answer therefore then becomes 0.0016560 (notice that we fill the blank spaces with zeros). However, this time we also need to drop the zero off of the end because it is a decimal. Decimals should never have zeros at the end. So the final correct answer becomes 0.001656.

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