Q1(a). Percentage relative error of a balance reading

Answer in brief

True mass = 10.0 g; relative error = (9.5 − 10.0)/10.0 × 100 = −5.0 %, so the balance reads 5 % low.

Key points

• True (actual) mass: xt = 9.5 + 0.5 = 10.0 g.
• Absolute error = measured value − true value, with its sign: E = 9.5 − 10.0 = −0.5 g.
• Relative error = absolute error as a percentage of the true value: Er = −0.5/10.0 × 100 = −5.0 % (−50 parts per thousand).
• The negative sign is kept: the result is lower than the true value; relative accuracy = 95 %.
• A balance that reads low is a determinate (systematic) error; it is removed by calibration with standard masses.