Question

Round off the following quantities to the indicated number of significant figures. (a) \(17.2509 \mathrm{~cm}\) (4 significant figures) (b) \(168.51 \mathrm{lb}\) (3 significant figures) (c) \(500.22^{\circ} \mathrm{C}\) ( 3 significant figures) (d) 198.500 oz ( 3 significant figures)

Short answer

Question: Round the following values to the specified number of significant figures: (a) \(17.2509 \mathrm{~cm}\) to 4 significant figures. (b) \(168.51 \mathrm{lb}\) to 3 significant figures. (c) \(500.22^{\circ} \mathrm{C}\) to 3 significant figures. (d) \(198.500 \mathrm{~oz}\) to 3 significant figures. Answer: (a) \(17.25 \mathrm{~cm}\) (b) \(169 \mathrm{lb}\) (c) \(500^{\circ} \mathrm{C}\) (d) \(199 \mathrm{~oz}\)

Step-by-step solution

Determine the Significant Figures

To begin, we can determine the number of significant figures in each given value. Significant figures are any non-zero digit or any zeros between non-zero digits. (a) \(17.2509 \mathrm{~cm}\) has 6 significant figures. (b) \(168.51 \mathrm{lb}\) has 5 significant figures. (c) \(500.22^{\circ} \mathrm{C}\) has 5 significant figures. (d) \(198.500 \mathrm{~oz}\) has 6 significant figures.

Round to the given number of Significant Figures

Now, we will round each value to the requested number of significant figures. Keep in mind the rules for rounding: if the digit after the last significant digit is equal to or greater than 5, round up; if it's less than 5, keep it as is. (a) Round \(17.2509 \mathrm{~cm}\) to 4 significant figures: We want to keep 4 significant figures: \(17.25\), the next digit is 0, so we don't round up. Answer: \(17.25 \mathrm{~cm}\) (b) Round \(168.51 \mathrm{lb}\) to 3 significant figures: We want to keep 3 significant figures: \(168\), the next digit is 5, so we round up. Answer: \(169 \mathrm{lb}\) (c) Round \(500.22^{\circ} \mathrm{C}\) to 3 significant figures: We want to keep 3 significant figures: \(500\), the next digit is 2, so we don't round up. Answer: \(500^{\circ} \mathrm{C}\) (d) Round \(198.500 \mathrm{~oz}\) to 3 significant figures: We want to keep 3 significant figures: \(198\), the next digit is 5, so we round up. Answer: \(199 \mathrm{~oz}\)