To determine which of the given numbers is expressed to three significant figures, we first need to understand what significant figures are. Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. ### Analyzing Each Option **Option A: 0.00456** - The leading zeros (0.00) are not significant. - The significant figures start from the first non-zero digit, which is 4. - Therefore, the significant figures are 4, 5, and 6. - This number has **three significant figures**: 4, 5, and 6. **Option B: 123.45** - All digits in this number are non-zero. - Therefore, the significant figures are 1, 2, 3, 4, and 5. - This number has **five significant figures**: 1, 2, 3, 4, and 5. **Option C: 0.98765** - The leading zero (0.) is not significant. - The significant figures start from the first non-zero digit, which is 9. - Therefore, the significant figures are 9, 8, 7, 6, and 5. - This number has **five significant figures**: 9, 8, 7, 6, and 5. **Option D: 5.6700** - All digits are significant here. The trailing zeros after the decimal point (00) are significant because they indicate precision. - Therefore, the significant figures are 5, 6, 7, 0, and 0. - This number has **five significant figures**: 5, 6, 7, 0, and 0. ### Conclusion From the analysis above, we can see that: - **Option A (0.00456)** has **three significant figures**. - **Option B (123.45)** has **five significant figures**. - **Option C (0.98765)** has **five significant figures**. - **Option D (5.6700)** has **five significant figures**. Thus, the correct answer is **A. 0.00456**. ### Why Other Options Are Incorrect - **Option B (123.45)**: This option has five significant figures, which exceeds the requirement of three. - **Option C (0.98765)**: This option also has five significant figures, which is more than three. - **Option D (5.6700)**: This option has five significant figures due to the trailing zeros, which also exceeds three. ### Summary - Significant figures include all non-zero digits, zeros between significant digits, and trailing zeros in decimal numbers. - The leading zeros in a decimal number are not counted as significant figures. - The only option with exactly three significant figures is **0.00456**. - Always count significant figures carefully, especially in decimal numbers and when trailing zeros are involved. ### Revision Summary - Significant figures include all non-zero digits and certain zeros. - Leading zeros are not significant. - Trailing zeros in a decimal number are significant. - The correct answer for three significant figures in the options provided is **A. 0.00456**.