Theory question 104
Fractions, Decimals and ApproximationA carpenter was told to make a rectangular desk with top, of dimension 50cm by 40cm. The carpenter actually made the desk 60cm by 35cm.
(a) Calculate the percentage error in the: (i) length and the breadth; (ii) area of the table top.
(b) Find the product of the two errors in (a)(i).
Show the model answer
Model answer
(a)(i) Length: error = 10cm, 10/50 × 100 = 20%. Breadth: error = 5cm, 5/40 × 100 = 12.5%
(ii) Intended area = 2000cm2, actual = 2100cm2; error = 100cm2; 100/2000 × 100 = 5%
(b) 20 × 12.5 = 250 (as fractions 0.2 × 0.125 = 0.025)
Explanation
Percentage error = error ÷ the correct (intended) value × 100.