Question

Subtract $ 2.5 \times {10^4} $ from $ 3.9 \times {10^5} $ and give the answer to the correct number of significant figures.
(A) $ 3.6 \times {10^6} $
(B) $ 3.6 \times {10^5} $
(C) $ 36 \times {10^5} $
(D) $ 36 \times {10^6} $

Answer 1

Hint: It is very important to understand the concept of significant figures. In most of the experimental measurements there exists some kind of uncertainty associated with them. This uncertainty directly or indirectly affects the precision and accuracy of measurements.

Complete step-by-step solution
The precision can be defined as the closeness of two or more quantities to each. This can also be defined as the level of measurement which when repeated provides the same result.
While accuracy is defined as the level of measurement that provides true and consistent results. The obtained results are always in agreement with the true or correct results.
To find the value by subtraction between the given value $ 2.5 \times {10^4} $ from $ 3.9 \times {10^5} $ . Before subtracting the values given some laws of the significant figures are to be followed. They are:
All the non-zero digits in the given values are significant.
All the zeros between the non-zero digits are considered as significant.
The final zero in the decimal portion is considered as only significant.
First, we have to evaluate the value of $ 2.5 \times {10^4} $ and write it in proper power $ {10^5} $ to match the power of the other given number $ 3.9 \times {10^5} $ . Hence it can be written as
 $ = 2.5 \times {10^4} = 0.25 \times {10^5} $
Now the subtraction can be evaluated between the numbers as
 $ 3.9 \times {10^5} - 0.25 \times {10^5} = \left( {3.9 - 0.25} \right) \times {10^5} $
 $ \Rightarrow \left( {3.9 - 0.25} \right) \times {10^5} = 3.65 \times {10^5} $
Now approximating the digits we get as $ 3.65 \times {10^5} \approx 3.6 \times {10^5} $ .
Therefore the required value by the subtraction $ 2.5 \times {10^4} $ from $ 3.9 \times {10^5} $ is given as $ 3.65 \times {10^5} $ .
Hence the option (B) is the correct answer.

Note
Significant figures can be considered as the number of important single digits and it is an integral part of mathematical and statistical calculations, which deal with numerical accuracy and precision, and estimating exactness about the end outcome is always crucial.