UPSC Combined Geo-Scientist, Mains · 2020 · Mains Paper III

Q1(a). Significant figures

Question

Round appropriately: (i) 2.4+0.010+6.24; (ii) 3.6-0.020-5.14; (iii) 22(5.42)/100.0; (iv) log (5.000×10⁻⁴); (v) antilog 12.5.

(i) 8.7; (ii) -1.6; (iii) 1.2; (iv) -3.3010; (v) 3×10¹².

Addition/subtraction is rounded to the least precise decimal place. The unrounded first two values are 8.650 and -1.560, hence one decimal place in each.
Multiplication/division is limited by the factor with fewest significant figures: 22 has two, so 1.1924 becomes 1.2.
A logarithm of a four-significant-figure number has four decimal places: log (0.0005000)=-3.301029996….
Conversely, one decimal place in 12.5 implies one significant figure in its antilogarithm. Thus 10^12.5=3.162…×10¹² is reported as 3×10¹².

The full model answer

As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.

CoversSignificant figuresNumerical reporting