5. For each of the following measured values, find the maximum absolute error, the lower limit and the upper limit of its actual value. (a) 2.4 km (cor. to the nearest 0.1 km ) (b) 1400 mL (cor. to 3 sig. fig.) (c) 15.70 s (cor. to 4 sig. fig.) Solution

: To find the maximum absolute error, lower limit, and upper limit of the actual value for each measured value, we need to consider the precision of the measurement and the significant figures. (a) 2.4 km (cor. to the nearest 0.1 km) Step 1: Determine the precision of the measurement. The measurement is rounded to the nearest 0.1 km, which means the precision is 0.1 km. Step 2: Calculate the maximum absolute error. The maximum absolute error is half of the precision, so it is 0.1 km / 2 = 0.05 km. Step 3: Calculate the lower limit of the actual value. The lower limit is the measured value minus the maximum absolute error, so it is 2.4 km - 0.05 km = 2.35 km. Step 4: Calculate the upper limit of the actual value. The upper limit is the measured value plus the maximum absolute error, so it is 2.4 km + 0.05 km = 2.45 km. Therefore, for the measured value of 2.4 km, the maximum absolute error is 0.05 km, the lower limit is 2.35 km, and the upper limit is 2.45 km. (b) 1400 mL (cor. to 3 sig. fig.) Step 1: Determine the precision of the measurement. The measurement is given to 3 significant figures, which means the precision is 1 mL. Step 2: Calculate the maximum absolute error. The maximum absolute error is half of the precision, so it is 1 mL / 2 = 0.5 mL. Step 3: Calculate the lower limit of the actual value. The lower limit is the measured value minus the maximum absolute error, so it is 1400 mL - 0.5 mL = 1399.5 mL. Step 4: Calculate the upper limit of the actual value. The upper limit is the measured value plus the maximum absolute error, so it is 1400 mL + 0.5 mL = 1400.5 mL. Therefore, for the measured value of 1400 mL, the maximum absolute error is 0.5 mL, the lower limit is 1399.5 mL, and the upper limit is 1400.5 mL. (c) 15.70 s (cor. to 4 sig. fig.) Step 1: Determine the precision of the measurement. The measurement is given to 4 significant figures, which means the precision is 0.01 s. Step 2: Calculate the maximum absolute error. The maximum absolute error is half of the precision, so it is 0.01 s / 2 = 0.005 s. Step 3: Calculate the lower limit of the actual value. The lower limit is the measured value minus the maximum absolute error, so it is 15.70 s - 0.005 s = 15.695 s. Step 4: Calculate the upper limit of the actual value. The upper limit is the measured value plus the maximum absolute error, so it is 15.70 s + 0.005 s = 15.705 s. Therefore, for the measured value of 15.70 s, the maximum absolute error is 0.005 s, the lower limit is 15.695 s, and the upper limit is 15.705 s.