Example 1 – OK….how would you start looking at this problem?


Well, it looks quite complicated but imagine for a moment that these were not decimal numbers and you were looking at being asked to multiply 137 x 64.


Going back to the previous section where we “long multiplied” numbers like this you would attack it quite simply by starting off 7 times 4 equals 28, put the 8 in the box carried the 2 and so on.


Your answer would be 8768, but the answer to this question is actually 87.68, does anything standout?


In fact the actual answer is 100 times smaller than the answer we gave when we did not consider this to be decimal sum. What we did in fact do is multiply 13.7 x 10 to get rid of the decimal, then we multiplied 6.4 x 10 to get rid of the decimal again but this gave us an answer which was 10×10 times larger than we wanted, so in the end we had to divide the answer by 100 to make it right.


Now if you think about it, we are starting to develop the technique already for dealing with decimals, make them into whole numbers then do the multiplication but remember to turn them back into decimals at the end when we have the answer. The trick here is quite simple:


How many decimal places in 13.7? The answer of course is one.


How many decimal places in 6.4? The answer of course is one.


What is 1+1? The answer of course is two.


So the procedure is….. to multiply 2 numbers together which have one decimal place each, take out the decimal points and treat them as integer numbers (that is whole numbers), multiply them together and then rewrite your answer to 2 decimal places which is the sum of the two one decimal places you adjusted for in the beginning.


As always, a diagram might help to explain a bit better:

Let’s really jump in at the deep end now and do a far more complicated than the one above, simply to highlight this “adding up of the decimal places” method.


This time we are being asked to multiply 45.137 x 6.4345 but this isn’t really any more complicated than the previous one, it might just look it.


The first thing that we do is take out the decimal places from 45.137, and to do this we must multiply it by a thousand, but the trick is we don’t actually have to do this, just remember “3”


We do the same thing with 6.4345, we would multiply it by 10,000, but again the trick is we don’t have to, just remember “4” and then remember that “3” + “4” equal “7”.


Okay, now multiply 45,137 x 64,345 and you come to an answer of 2,904,340,265. However, this answer is many orders of magnitude (10 million times) too big, remember the 7? Well, insert that 7 decimal places starting from the 5 on the extreme right and you will find your answer is in fact 290.4340265


So, 45.137×6.4345 equals 290.4340265 to 7 decimal places, check it on a calculator and you’ll find it’s right.

General rule:


If you’re multiplying 2 numbers together, the first number having X decimal places and the second number having Y decimal places:


  • make a note of X and Y, and add them together
  • remove the decimal points and treat the 2 numbers as whole numbers
  • multiply the 2 whole numbers together
  • replace the decimal point at position X plus Y digits from the right