d) Expand (1.002)7 using binomial theorem correct to 7significant figures

The binomial theorem states that (a+b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k=0 to n.

Here, a=1, b=0.002, and n=7.

The binomial expansion of (1.002)^7 up to the 7th term is:

= 1^7 * (0.002)^0 * (7 choose 0) + 1^6 * (0.002)^1 * (7 choose 1) + 1^5 * (0.002)^2 * (7 choose 2) + 1^4 * (0.002)^3 * (7 choose 3) + 1^3 * (0.002)^4 * (7 choose 4) + 1^2 * (0.002)^5 * (7 choose 5) + 1^1 * (0.002)^6 * (7 choose 6) + 1^0 * (0.002)^7 * (7 choose 7)

= 1 + 0.014 + 0.000147 + 0.00000147 + 0.0000000106 + 0.0000000000532 + 0.00000000000159 + 0.0000000000000256

= 1.014148481659

Rounding to 7 significant figures, the answer is 1.014148.