Question

In the final answer of the expression$\dfrac{{(29.2 - 20.2)(1.79 \times {{10}^5})}}{{1.37}}$​. The number of significant figures is:
A. 1
B. 2
C. 3
D. 4

Answer 1

Hint:Significant figures refer to the numbers which provide a meaningful measurement to an experiment. Three rules must be kept in mind while determining the significant figures in a number:
1. Any zeros between the two significant digits are always significant.
2. Non-zero digits are always significant.
3. A final zero or a trailing zero in the decimal portion only, are significant.

Complete answer:
The given expression is: $\dfrac{{(29.2 - 20.2)(1.79 \times {{10}^5})}}{{1.37}}$
- In case of addition and subtraction, carefully look at the places of the decimal point. Add or subtract normally and then you must round the answer to the LEAST number of places of the decimal point of the number in the question. While in case of multiplication and division, the LEAST number of significant figures in any number determines the number of the significant figures in answer.
- The given expression can be solved as: $\dfrac{{(29.2 - 20.2)(1.79 \times {{10}^5})}}{{1.37}} = \dfrac{{9.0 \times 1.79 \times {{10}^5}}}{{1.37}}$
In the mathematical operations involving the significant figures, always remember that the answer is reported in such a manner that it reflects the reliability of least precise operation.
Thus, in the present case, the last precise term is 9.0 which has two significant figures.

Hence, the correct answer is Option B.

Note:
Keep in mind that the rules for addition/subtraction are different from multiplication/division. Mostly students get confused and result in the error by swapping the two sets of rules. And another common error is to use one rule for both of the types of operations.