Question

The result of the operation \[{\text{2}}{\text{.5 x 1}}{\text{.25}}\] should be which of the following on the basis of significant figures?
A.3.125
B.3.13
C.3.1
D.31.25

Answer 1

Hint: Significant numbers are used to depict the accuracy and precision in data. It can be determined from the five rules that are commonly used in the scientific field.

Complete step by step answer:
The rules to determine the significant digits are given below:
All non-zero digits are significant.Zeros between non-zero digits are significant.
A trailing zero or final zero in the right of the decimal portion only are significant.
Leading zeroes are not significant.
For a number in scientific notation: \[{\text{Y x 1}}{{\text{0}}^{\text{x}}}\], all digits comprising Y will be significant by the above given rules; "10" and "x" are not significant.
In case of operations like multiplication or division performed, the final answer should have the same number of significant numbers which will be the least number of significant numbers given in the question.
For the given problem, operation of multiplication is carried out.
\[{\text{2}}{\text{.5 x 1}}{\text{.25 = 3}}{\text{.125}}\]
But as stated, the final result should have the least number of significant numbers given in the question.
In the question 2.5 has 2 significant numbers and 1.25 has 3 significant numbers. Hence the final answer should have only 2 significant numbers.
\[ \Rightarrow {\text{2}}{\text{.5 x 1}}{\text{.25 = 3}}{\text{.1}}\]
Now, the final answer has only 2 significant numbers.

So, the correct option is C.

Note:
In case of operations like addition and subtraction performed, the final answer should have the same number of decimal places which will be the least number of decimal places given in the question. Hence, significant numbers are not considered in the final result like multiplication or division operation.