A student measures certain lengths using a meter scale having least count equal to 1 mm. Which one of the following measurements is more precise ?
0$cdot$50 mm
29$cdot$07 cm
0$cdot$925 m
910 mm
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-2 – 2019
Let’s express all measurements in mm:
A) 0.50 mm – recorded to two decimal places. This suggests precision to 0.01 mm.
B) 29.07 cm = 290.7 mm – recorded to one decimal place in mm. This suggests precision to 0.1 mm.
C) 0.925 m = 925 mm – recorded to the nearest whole number in mm. This suggests precision to 1 mm.
D) 910 mm – recorded to the nearest whole number in mm (assuming the trailing zero is significant). This suggests precision to 1 mm.
Comparing the implied precisions: A (0.01 mm) < B (0.1 mm) < C and D (1 mm). Although measuring 0.50 mm or achieving 0.01 mm precision with a 1 mm least count scale is highly questionable or impossible in practice for a single measurement, the *way the number is recorded* implies a certain level of precision. Among the given options, 0.50 mm is recorded with the highest implied precision (to the hundredths of a millimeter). Therefore, as recorded, it is the most precise measurement listed.
– With a scale of 1 mm least count, readings are usually taken to the nearest 1 mm or estimated to the nearest 0.1 mm.
– The number of decimal places in the unit of the least count often suggests the level of precision in the recorded value.
– Recording 290.7 mm suggests uncertainty in the tenths place, typically interpreted as $\pm 0.05$ mm, which is a reasonable estimation precision with a 1 mm scale.
– Recording 925 mm or 910 mm suggests uncertainty in the units place, typically interpreted as $\pm 0.5$ mm, which is standard for direct readings.
– Despite the practical limitations, the recording 0.50 mm implies the highest level of precision among the given options.