To determine which of the given numbers has three significant figures, we need to understand the rules for identifying significant figures in a number. Let's analyze each option step by step. ### Significant Figures Rules: 1. **Non-zero digits** are always significant. For example, in the number 123, all three digits (1, 2, and 3) are significant. 2. **Leading zeros** (zeros before the first non-zero digit) are not significant. For example, in 0.00456, the leading zeros (0.00) do not count as significant figures. 3. **Captive zeros** (zeros between non-zero digits) are significant. For example, in 105, the zero is significant because it is between the 1 and the 5. 4. **Trailing zeros** in a decimal number are significant. For example, in 0.0704, the zero after the 7 is significant because it is after a decimal point and follows a non-zero digit. 5. **Trailing zeros** in a whole number without a decimal point are not considered significant unless specified by a decimal point. For example, in 1500, the zeros may or may not be significant depending on the context. ### Analyzing Each Option: **A. 0.00456** - The leading zeros (0.00) are not significant. - The digits 4, 5, and 6 are significant. - **Total significant figures: 3** (4, 5, 6). **B. 1230** - The digits 1, 2, and 3 are significant. - The trailing zero (0) is ambiguous without a decimal point. It could be significant or not, depending on the context. - **Total significant figures: 3 or 4** (1, 2, 3 are definitely significant; the 0 is uncertain). **C. 0.0704** - The leading zeros (0.0) are not significant. - The digits 7, 0, and 4 are significant. - **Total significant figures: 4** (7, 0, 4). **D. 1500** - The digits 1 and 5 are significant. - The trailing zeros (00) are ambiguous without a decimal point. They may or may not be significant. - **Total significant figures: 2 or 4** (1, 5 are definitely significant; the 0s are uncertain). ### Conclusion: The only option that clearly has three significant figures is **A. 0.00456**. ### Why Other Options Are Incorrect or Weaker: - **B. 1230**: While it can be interpreted as having three significant figures, the ambiguity of the trailing zero makes it less definitive. - **C. 0.0704**: This has four significant figures, not three. - **D. 1500**: This can be interpreted as having two or four significant figures, but not definitively three. ### Revision Summary: - Significant figures include all non-zero digits, captive zeros, and trailing zeros in decimal numbers. - Leading zeros are not counted as significant figures. - The number 0.00456 has exactly three significant figures. - Be cautious with trailing zeros in whole numbers; they may be ambiguous without context.