Significant Figures

Step 1: Understanding significant figures.
Significant figures are the digits in a number that carry meaningful information about its precision. The following rules apply to counting significant figures:
1. Non-zero digits are always significant.
2. Any zeros between significant digits are significant.
3. Leading zeros (zeros before the first non-zero digit) are not significant.
4. Trailing zeros in a decimal number are significant.
Step 2: Analyze each statement.
A. 6.405 has four significant figures.
This is correct. The digits 6, 4, 0, and 5 are all significant in this number.
B. 12300 has five significant figures.
This is incorrect. The trailing zeros in the number 12300 are not significant because there is no decimal point explicitly shown. It has only three significant figures: 1, 2, and 3.
C. 0.00421 has five significant figures.
This is incorrect. The leading zeros are not significant. The significant figures are 4, 2, and 1, so the number has three significant figures.
D. 4.500 has four significant figures.
This is correct. The trailing zeros after the decimal point are significant because they show the precision of the measurement.
Step 3: Conclusion.
The correct answer is (2) A and D only because both statements A and D are true.