Exercise 1.12

Transcript

Exercise 1.12 The mass of a box measured by a grocer’s balance is 2.30 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is (a) the total mass of the box, (b) the difference in the masses of the pieces to correct significant figures ? Given Mass of box = 𝒎_(𝒃𝒐𝒙) = 2.30 kg Mass of 1^(st) gold piece = 𝒎_(𝟏)= 20.15 g = 20.15 × 10^(–3) kg = 2.015 × 10^(–2) kg Mass of 2^(nd) gold piece = 𝒎_(𝟐) = 20.17 g = 20.17 × 10^(–3) kg = 2.017 × 10^(–2) kg Since we are adding and subtracting here, we write m_(1) and m_(2) in decimals Now, 𝑚_(1)= 0.02015 kg 𝑚_(2)= 0.02017 kg (a) the total mass of the box, Total mass of box = 𝑚_(𝑏𝑜𝑥) + 𝑚_(1) + 𝑚_(2) = 2.30 + 0.02015 + 0.02017 = 2.34032 kg Since we are adding numbers, we check lowest decimal places Now, 2.30 has 2 decimal places, so the final answer will have 2 decimal places Thus, Total mass of box = 2.34 kg (b) the difference in the masses of the pieces to correct significant figures ? Now, Difference in gold masses = m_(2) – m_(1) = 0.02017 – 0.02015 = 0.00002 kg Since we are subtracting numbers, we check lowest decimal places Now, both numbers have 5 decimal places, so the final answer will have 5 decimal places Thus, Difference in gold masses = 0.00002 kg Or we can write in grams also Difference in gold masses = m_(2) – m_(1) = 20.17 – 20.15 = 0.02 g Here, we have 2 decimal places in both numbers So, final answer has 2 decimal places = 2.017 × 10^(–2) kg Since we are adding and subtracting here, we write m_(1) and m_(2) in decimals Now, 𝑚_(1)= 0.02015 kg 𝑚_(2)= 0.02017 kg (a) the total mass of the box, Total mass of box = 𝑚_(𝑏𝑜𝑥) + 𝑚_(1) + 𝑚_(2) = 2.30 + 0.02015 + 0.02017 = 2.34032 kg Since we are adding numbers, we check lowest decimal places Now, 2.30 has 2 decimal places, so the final answer will have 2 decimal places Thus, Total mass of box = 2.34 kg (b) the difference in the masses of the pieces to correct significant figures ? Now, Difference in gold masses = m_(2) – m_(1) = 0.02017 – 0.02015 = 0.00002 kg Since we are subtracting numbers, we check lowest decimal places Now, both numbers have 5 decimal places, so the final answer will have 5 decimal places Thus, Difference in gold masses = 0.00002 kg Or we can write in grams also Difference in gold masses = m_(2) – m_(1) = 20.17 – 20.15 = 0.02 g Here, we have 2 decimal places in both numbers So, final answer has 2 decimal places