Significant Figures 973Ac3

1. **State the problem:** We want to understand how to determine the number of significant figures in a given number and how to round numbers to a specific number of significant figures. 2. **Important rules for significant figures:** - All non-zero digits are significant. - Zeros between non-zero digits are significant. - Leading zeros are not significant. - Trailing zeros in a decimal number are significant. 3. **Example:** Consider the number $0.004560$. 4. **Step 1: Identify significant digits:** - Leading zeros ($0.00$) are not significant. - Digits $4$, $5$, and $6$ are significant. - The trailing zero after $6$ is significant because it is after the decimal point. - So, $0.004560$ has 4 significant figures. 5. **Step 2: Rounding to significant figures:** - Suppose we want to round $0.004560$ to 3 significant figures. - The first 3 significant figures are $4$, $5$, and $6$. - The next digit is $0$, which is less than 5, so we do not round up. - The rounded number is $0.00456$. 6. **Step 3: Using the formula for rounding:** - To round a number to $n$ significant figures, identify the $n$th significant digit. - Look at the digit immediately after it. - If that digit is 5 or more, increase the $n$th digit by 1. - Otherwise, leave it as is. 7. **Summary:** - Count significant figures using the rules. - Round numbers by looking at the digit after the last significant figure desired. This process helps ensure precision and accuracy in scientific calculations.