Math operations on whole numbers or integers are simple and can be done without much difficulties. Example: 5 + 4 x 3 = 60 is simple enough for anyone. How decimal numbers?
Try doing 0.15 x 0.4. This is slightly more difficult (for some people). Why so?
Because of the decimal places!
However, if you understand the meaning of this decimal place or the decimal point, the math calculation becomes simple and straight forward.
Meaning of decimal point:
Let us take an example. 0.5 = 1/2. It is a fraction written in another form.
How about 0.1? Mentally, we know it is 1/10. Good!
How about 0.14? This may catch some off-guard.
The trick is simple. Make use of the 10, 100, or multiples of 10 at the denominator.
Therefore 0.14 can be written in fraction as 14 / 100.
0.45 = 45 / 100
0.245 = 245 / 1000
0.012 = 12 / 1000
0.6 = 6 / 10
See the pattern of the denominator with relation to the number of significant places (numbers after the decimal point).
If there are 3 significant places, then you use 3 "0"s for the denominator, meaning, 1000.
If there are 2 significant places, then you use 2 "0"s, that is, 100.
With this understanding of converting decimal to fraction, we can proceed to do math operation on decimal numbers.
We will not do addition and subtraction here as they are simply too easy.
(0.1 + 0.4 => 0.5 Too simple, right?)
Let's do 0.4 x 0.15.
Watch out now! Since integers are much more easy to handle, both mentally and written, let's do the multiplication WITHOUT the decimal places. That is, 4 X 15.
4 x 15 = 60. But that is not final. What we have simplified is the removal of the decimal points.
We still owe the original question our denominator!
0.4 = 4 / 10 and 0.15 = 15 / 100. This results in the final denominator as 10 x 100 = 1000.
To obtain the final answer to 0.4 x 0.15 is simply 4 x 15 / 1000 = 60 / 1000.
Therefore 0.4 x 0.15 = 60 / 1000 = 0.06
We obtained 0.06 (the final answer) by shifting the decimal point to the left (of numerator 60) by 3 places.
Steps of the trick:
Change the decimal numbers to the easily workable integers.
Use multiple of 10 as the denominator as it is easy to shift the decimal point later.
Multiply the converted integers.
Finally shift the decimal point to the left by the number of "0" in the denominator.
0.3 x 0.12 = 3 x 12 / (10 x 100) => 36 / 1000 ==> 0.036 (final answer)
Advantage of this method:
The removal of decimal point reduces the confusion of number of significant places during the intermediate computation. It, therefore, reduces the chance of making mistakes by breaking the calculations into more focused and dedicated steps.
Knowing the weak point of yourselves is half the battle won!