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 any 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: 0.78901** - The leading zeros (0.) are not significant. - The significant figures start from the first non-zero digit, which is 7. - Therefore, the significant figures are 7, 8, 9, 0, and 1. - This number has **five significant figures**: 7, 8, 9, 0, and 1. **Option D: 56000** - This number has trailing zeros, which can be ambiguous without a decimal point. - If written as 56000 without a decimal, it is typically considered to have **two significant figures** (5 and 6). - If it were written as 56000. or 5.6000 × 10^4, it would indicate more significant figures, but as it stands, it has **two significant figures**. ### Conclusion Based on the analysis: - **Option A (0.00456)** is the only number that is expressed to three significant figures. ### Why Other Options Are Incorrect - **Option B (123.45)** has five significant figures, not three. - **Option C (0.78901)** also has five significant figures, not three. - **Option D (56000)** has two significant figures unless specified otherwise, so it does not meet the requirement of three significant figures. ### Summary - Significant figures include all non-zero digits, zeros between significant digits, and trailing zeros in decimal numbers. - **Option A (0.00456)** is the only number with three significant figures. - **Options B and C** have five significant figures, while **Option D** has two significant figures. ### Revision Summary - Significant figures are crucial for precision in measurements. - Leading zeros are not counted as significant figures. - Trailing zeros in whole numbers without a decimal point can lead to ambiguity. - Always check the context of the number to determine the correct count of significant figures.