In Example 7, change 0.97 to 0.98.

Data from Example 7

Approximate the value of 0.97⁷ by use of the binomial series. We note that 0.97 = 1 − 0.03, which means 0.97⁷ = [1 + (−0.03)]⁷ . Using four terms of the binomial series, we have

From a calculator, we find that 0.977 = 0.807983 (to six decimal places), which means these values agree to four significant digits with a value 0.8080. Greater accuracy can be found using the binomial series if more terms are used.

0.977 [1 + (-0.03)]' = 7(6)(5) (-0.03)3 3! 0.000945= 0.807955 7(6) = 1 +7(-0.03) + (-0.03) + 2! = 1 0.21 +0.0189