How would you multiply decimals?

Answer 1

The following method works only for terminating decimals.

Let n be the number of digits after (to the right of) the decimal point in the first number in the multiplication, and let m be the number of digits after the decimal point in the second number. Let p = n + m.

Now remove the decimal points and mutiply the two integer numbers together. [Unlike some misleading answers on this site, you do not need to algn the decimal points.] When you have the answer, insert the decimal point so that you have p digits after the decimal point.

For example,

2.718*13.45

n = 3, m = 2 and so p = 2+3=5

2718*1345 = 3655710

Inserting the decimal point so that there are 5 digits after the decimal point gives

36.55710 which can then be simplified to 36.5571: do not delete the trailing 0s until after you have placed the decimal point in the correct position.

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For recurring decimals, multiply the two numbers ignoring the decimal points. Do a second calculation using the two numbers rounded to only 1 or 2 significant digits (using the above method if necessary). This will give you an order of magnitude for the answer. Use this second answer to give you a hint about where the decimal point should go. This method will work for all decimals.

Finally, you may be lucky and see a recurrence pattern in the answer or you may not.

For example,

12.1666...*0.031

121666*31 = 377166646

The two numbers, to 1 sd are 10 and 0.03

Now n = 0, m = 2 and so p = 0+2=2

10*3 = 30 and so, inserting the decimal point so that there are two digits after it gives 0.03

Therefore, the answer is approximately 0.03.

So the answer to the decimal multiplication is 377166646 "converted" to 0.0377166646. Finally, I can see the recurrence pattern and can write the answer as 0.03771666...