Multiple choice

The approximate value of $\dfrac{(3.03)^3}{27}$

  1. $1.03$
  2. $1.01$
  3. $3.03$
  4. $3.01$
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A Correct answer
Explanation

3.03^3 = (3 + 0.03)^3 = 3^3 + 3(3^2)(0.03) + 3(3)(0.03^2) + 0.03^3 = 27 + 0.81 + 0.0081 + 0.000027 = 27.818127. Dividing by 27 gives 1.030301, which is approximately 1.03.

AI explanation

We can rewrite the expression as $\frac{(3.03)^3}{27} = \left(\frac{3.03}{3}\right)^3 = (1.01)^3$. Using the binomial approximation $(1 + x)^n \approx 1 + nx$ for small $x$, we get $(1.01)^3 \approx 1 + 3(0.01) = 1.03$. Therefore, the approximate value is $1.03$.

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