Significant Figures

Significant figures are the digits in a number that carry meaningful information about the precision or accuracy of the measurement. They are used to indicate the level of certainty in a measurement and to ensure that calculations are performed with the correct level of precision.

Counting Significant Figures

To count the number of significant figures in a number, the following rules are applied:

1. Non-zero digits are always significant. For example, in the number 123.45, all five digits (1, 2, 3, 4, and 5) are significant.

2. Zeros between non-zero digits are also significant. In the number 1002, all four digits (1, 0, 0, and 2) are significant.

3. Leading zeros (zeros to the left of the first non-zero digit) are not significant. In the number 0.0056, only two digits (5 and 6) are significant.

4. Trailing zeros (zeros to the right of the last non-zero digit) are significant if there is a decimal point present. In the number 100.0, all four digits (1, 0, 0, and 0) are significant.

5. Trailing zeros without a decimal point are not significant. In the number 1000, only one digit (1) is significant.

Analysis of the Given Number

The given number is 0.010100 x 103.

To determine the number of significant figures in this number, we need to consider both parts of the expression separately.

1. 0.010100: This number has five significant figures (1, 0, 1, 0, and 0). Leading zeros are not significant, and trailing zeros are significant because there is a decimal point present.

2. 103: This number is an exact value and is considered to have an infinite number of significant figures.

Total Significant Figures

To find the total number of significant figures in the given number, we add the significant figures from both parts:

5 (from 0.010100) + infinite (from 103) = infinite

Therefore, the correct answer is option 'B' - 5 significant figures.