1 No measurement is perfect

• Accuracy of measurement is tied directly to scientific and technological progress, so humans keep improving methods and instruments.
• But it is impossible to obtain a 100 % exact measurement; there is always a margin of error, however small.
• When we measure the length of a room we usually find a small difference between the measured and the true value; the difference may be small or large depending on how carefully we measure.

Discussion exercise. Five students measured the same pencil: 10.1, 10.0, 9.8, 10.0, 10.0 cm.

• The readings are close but not identical → measurement involves small errors, and the best value is the mean: (10.1+10.0+9.8+10.0+10.0)/5 = 49.9/5 ≈ 10.0 cm.
• Possible reasons: reading the scale from the wrong angle, not starting at the zero mark, different judgment of where the end falls, a worn ruler end.
• A ruler graduated in 1 mm is more accurate than one graduated in 1 cm, because its smaller division allows a reading closer to the true length.