Use your expansion to evaluate 0.997^6, correct to four decimal place

Answer 1

We can use the binomial expansion formula to expand (1-0.003)^6 as follows:

(1-0.003)^6 = 1 - 6(0.003) + 15(0.003)^2 - 20(0.003)^3 + 15(0.003)^4 - 6(0.003)^5 + (0.003)^6

Now we can substitute 0.997 for (1-0.003) and simplify:

0.997^6 = 1 - 6(0.003)(0.997) + 15(0.003)^2(0.997)^2 - 20(0.003)^3(0.997)^3 + 15(0.003)^4(0.997)^4 - 6(0.003)^5(0.997)^5 + (0.003)^6(0.997)^6

Using a calculator, we get:

0.997^6 ≈ 0.9821

Therefore, 0.997^6, correct to four decimal places, is approximately 0.9821.