To determine the value of 0.00456 rounded to two significant figures, we need to follow a systematic approach. Let's break it down step-by-step. ### Step 1: Identify Significant Figures 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. In the number **0.00456**: - The leading zeros (the zeros before the 4) are not significant. They only serve to position the decimal point. - The significant figures start from the first non-zero digit, which is **4**. Thus, the significant figures in **0.00456** are **4, 5, and 6**. ### Step 2: Determine the Required Significant Figures We need to round the number to **two significant figures**. The first two significant figures in **0.00456** are **4** and **5**. ### Step 3: Rounding Process To round to two significant figures: - Look at the third significant figure, which is **6** (the digit immediately following the second significant figure, which is **5**). - According to rounding rules, if the digit after the last significant figure (in this case, the **6**) is **5 or greater**, we round up the last significant figure. Since **6** is greater than **5**, we round up the **5** to **6**. ### Step 4: Write the Rounded Number After rounding, the two significant figures of **0.00456** become **0.0046**. ### Conclusion Thus, the value of **0.00456** rounded to two significant figures is **0.0046**. ### Answer The correct option is **C. 0.0046**. ### Explanation of Other Options - **A. 0.0045**: This option is incorrect because it does not account for the rounding of the second significant figure (5) up to 6 due to the presence of the 6 in the third significant figure. - **B. 0.0050**: This option is incorrect because it represents a rounding to three significant figures (the trailing zero is significant), which is not what was asked for. - **D. 0.0047**: This option is incorrect because it incorrectly rounds the second significant figure down instead of up. ### Revision Summary - Significant figures include all non-zero digits and zeros between them or after a decimal point. - To round to a specific number of significant figures, look at the digit immediately following the last significant figure. - If that digit is 5 or greater, round up the last significant figure. - The correct rounding of **0.00456** to two significant figures is **0.0046**.