Significant Figures 408487

1. The problem asks to round the numbers $1.7844$ and $4.2872$ to a certain number of significant figures. 2. Significant figures are the digits in a number that carry meaning contributing to its precision. When rounding, we keep the specified number of significant digits and adjust the last digit accordingly. 3. Since the problem does not specify how many significant figures to round to, we assume the most common cases: - For $1.7844$ rounded to 3 significant figures: $$1.7844 \approx 1.78\cancel{4}4 \to 1.78\textbf{4} \to 1.78\textbf{4} \to 1.78\textbf{4}$$ Actually, rounding $1.7844$ to 3 significant figures means keeping the first three digits: $1$, $7$, and $8$, and rounding the third digit based on the fourth digit. The digits are $1.7 extbf{8}4 4$. The fourth digit is $4$, which is less than $5$, so we do not round up. So, $1.7844$ rounded to 3 significant figures is $1.78 extbf{4} \to 1.78 extbf{4}$ but since the third digit is $8$, the number is $1.78 extbf{4}$. Actually, the third digit is $8$, so the number rounded to 3 significant figures is $1.78 extbf{4}$. To clarify, the number is $1.7844$. The first three significant figures are $1$, $7$, and $8$. The fourth digit is $4$, less than $5$, so the third digit remains $8$. Therefore, $1.7844$ rounded to 3 significant figures is $1.78 extbf{4}$. But this is confusing, so let's write it properly: $$1.7844 \to 1.78\cancel{4}4 \to 1.78\text{(no change)} = 1.78\text{(rounded to 3 sig figs)}$$ Actually, $1.78$ has only 3 digits if we count the digits ignoring the decimal point: $1$, $7$, and $8$. So the answer is $1.78$. 4. For $4.2872$ rounded to 3 significant figures: The digits are $4$, $2$, $8$, $7$, $2$. The first three digits are $4$, $2$, and $8$. The fourth digit is $7$, which is greater than or equal to $5$, so we round the third digit up. $$4.2872 \to 4.28\cancel{7}2 \to 4.29$$ 5. Final answers: - $1.7844$ rounded to 3 significant figures is $1.78$. - $4.2872$ rounded to 3 significant figures is $4.29$.