Q.Perform the following operations : a. $3.971 \times 10^7 + 1.98 \times 10^4$ b. $1.05 \times 10^{-4} - 9.7 \times 10^{-5}$ c. $4.11 \times 10^{-3} + 8.1 \times 10^{-4}$ d. $2.12 \times 10^6 - 3.5 \times 10^5$

a. $3.971\times10^7 + 1.98\times10^4 = 3.971\times10^7 + 0.00198\times10^7 = 3.97298\times10^7$; rounding to match the coarser term's precision (0.001×10^7) gives $3.973\times10^7$.

b. $1.05\times10^{-4} - 9.7\times10^{-5} = 0.000105 - 0.000097 = 0.000008 = 8\times10^{-6}$ (only 1 significant figure survives, since the leading digits cancelled). …

Align each pair of numbers to the same power of ten before adding/subtracting the coefficients, then round the result …

• In part (b), not recognising that subtracting two close numbers causes a genuine loss of significant figures ('subtractive cancellation') — …