CPM Homework Help : PC Problem 8-108

Computer without a calculator. Lance forgot his calculator and needed to find the exact value of $1.1^{4}$ . He decided to use the binomial expansion by rewriting the expression as $\left(1 + 0.1\right)^{4}$ . Use the binomial formula to expand $\left(1 + 0.1\right)^{4}$ . Use your result to find the exact value of $1.1^{4}$ . (Recall that $0.1^{2} = 0.01, 0.1^{3} = 0.001$ )

Answer:

$= \left(1 + 0.1\right)^{4} = 1^{4} + 4\left(1\right)^{3}\left(0.1\right) + 6\left(1^{2}\right)\left(0.1^{2}\right) + \left(4\right)\left(1\right)\left(0.1^{3}\right) + 0.1^{4}$
$= 1 + \left(4\right)\left(0.1\right) + \left(6\right)\left(0.01\right) + \left(4\right)\left(0.001\right) + 0.0001$
$= 1 + 0.4 + 0.06 + 0.004 + 0.0001$
$= 1.4641$