Question

Given the numbers 786, 0.786 and 0.0786. The number of significant figures for the numbers is:
A 3, 4 and 5 respectively
B 3, 3 and 3 respectively
C 3, 3 and 4 respectively
D 3, 4 and 4 respectively

Answer 1

Hint: Apply the rules of the significant figures. Predict the digits that are significant and the digits that are not significant by using these rules of significant figures. It actually represents the number of digits that actually have some significance.

Complete Step by step answer: Write the rules for the determination of the significant figures:
If a digit is a non-zero digit, then it is always significant. For examples, the digits 7, 8 and 6 in the number 786 are significant. Similarly, the digits 7, 8 and 6 in the number 0.786 are significant. Similarly, the digits 7, 8 and 6 in the number 0.0786 are significant.
If a Zero is present between two non-zero digits, then it is significant. Thus, for example consider a number 706. The zero is present between two non-zero digits 7 and 6, Hence, this zero is significant.
If a zero is present on the right hand side of the number, then this zero is significant. In other words, if a trailing zero or final zero is present in the decimal portion, then it is significant. For example, consider the number 1.7860. In this number, the trailing zero is present in the decimal portion. Hence, this zero is significant. However, in the number 0.00786, none of the zeros is significant as the zeros are present in the preceding position. In the number 0.00786, the first non zero digit is 7. If any zero is present on the left hand side of the number, then this zero is not significant.
Now consider the given numbers 786, 0.786 and 0.0786. The number significant figures in these numbers is 3, 3 and 3 respectively.
In the number 786, all the digits 7,8 and 6 are non zero digits. Hence, these digits are significant.
In the number 0.786, the digits 7,8 and 6 are non zero digits. Hence, these digits are significant. The zero is present to the right of the decimal point. It is not significant.
In the number 0.0786, the digits 7,8 and 6 are non zero digits. Hence, these digits are significant. One zero is present to the right of the decimal point. It is not significant. The other zero is present in the preceding position. Hence, this zero is also not significant.

Hence, the correct option is the option (B).

Note: It must be noted that An experimental error is associated with a certain degree of uncertainty. The use of significant figures is a method for compensating the uncertainty in the measurement and to ensure the accuracy and precision in the measurement.