what is the best estimate for 3 * pi

Question

A. 9 1/7
B. 9 3/7
C. 6 3/7
D. 6 4/7

Answer 1

To estimate \(3 \times \pi\), we can use the approximation that \(\pi \approx 3.14\).

Calculating \(3 \times \pi\):

\[ 3 \times 3.14 = 9.42 \]

Now, let's compare this to the fractions given in the options:

1. A. \(9 \frac{1}{7}\)

   • \(9 \frac{1}{7} = 9 + \frac{1}{7} \approx 9.14\)

2. B. \(9 \frac{3}{7}\)

   • \(9 \frac{3}{7} = 9 + \frac{3}{7} \approx 9.43\)

3. C. \(6 \frac{3}{7}\)

   • \(6 \frac{3}{7} = 6 + \frac{3}{7} \approx 6.43\)

4. D. \(6 \frac{4}{7}\)

   • \(6 \frac{4}{7} = 6 + \frac{4}{7} \approx 6.57\)

From our calculations, \(3 \times \pi \approx 9.42\).

Comparing this value against the options, the closest estimate to \(9.42\) is:

B. \(9 \frac{3}{7}\), which is approximately \(9.43\).

Thus, the best estimate for \(3 \times \pi\) is B. \(9 \frac{3}{7}\).