Question

One number has three significant figures and another number has four significant figures. If these numbers are added, subtracted, multiplied, or divided, which operation can produce the greatest number of significant figures? The answer given is ADDITION. But why? How? Please explain and give examples. Thanks.

Answer 1

To know why the Operation "Addition" may give the maximum number of significant figures we will have to know the methods by which we express the result into appropriate number of significant digits after Addition,Subtraction,Multiplication and Division.

In both the Additioin and Subtraction process the result is expressed such that there should be smallest number of decimal places as present in any of the given number.

Let we add or subtract two values A and B.Let A has 2 decimal places and B has 3 decimal places then after either addition or subtraction(either A+B or A-B) the result should contain only 2 decimal places as B has.

Let we multiply or divide the same numbers A and B.Let A has 3 significant figure and B has 4 significant figure(here we count overall significant figures not only after decimal points).Then after either Multiplication or division(either AxB or A/B) the result should contain total 3 significant figures because B has minimum number of significant figures i.e. 3.

Now let us understand this with an example.

Let we have two numbers

A=5.34 (3 significant figures)

B=5.189 (4 significant figures

Addition:-

A+B=5.34+5.189=10.529

since A has minimum 2 significant figures after decimal(3 and 4) so result should also has 2 significant figure after decimal point so round off the result upto 2 decimal place we get-

A+B=10.53

so it has 4 significant figures.

Subtraction:-

A-B=5.34-5.189=0.151

round off the result upto 2 decimal place(same as in addition) we get-

A-B=0.15

So it has only 2 significant figures.

Multiplication:-             

AxB=5.34x5.189=27.70926

According to rule for multiplication result should have only 3 significant figure because B has least 3 significant figures so result is-

AxB=27.7

So it has only 3 significant figures.

Division:-

A/B=5.34/5.189=1.0291

round off to 3 significant figures (same as in multiplication) we get-

A/B=1.03

so It has 3 significant figures.

Hence from the above example we conclude that the chances for most significant figure is produced after Addition.