Question

which is the best estimate for 3 times pi? (1 point)
(6\frac{3}{7})
(6\frac{4}{7})
(9\frac{1}{7})
(9\frac{3}{7})

Explanation:

Step1: Recall the value of π

We know that \(\pi\approx\frac{22}{7}\) (a common fractional approximation for \(\pi\)).

Step2: Calculate \(3\times\pi\)

We need to find \(3\times\pi\approx3\times\frac{22}{7}\).
Calculate \(3\times\frac{22}{7}=\frac{66}{7}\).

Step3: Convert \(\frac{66}{7}\) to a mixed number

Divide \(66\) by \(7\): \(7\times9 = 63\), so \(66-63 = 3\). Thus, \(\frac{66}{7}=9\frac{3}{7}\)? Wait, no, wait. Wait, \(3\times\frac{22}{7}=\frac{66}{7}\), and \(7\times9 = 63\), \(66 - 63=3\), so \(\frac{66}{7}=9\frac{3}{7}\)? Wait, no, wait, \(\pi\approx3.14\), so \(3\times\pi\approx9.428\). Let's convert each option to decimal:

• \(6\frac{3}{7}=\frac{6\times7 + 3}{7}=\frac{45}{7}\approx6.428\)
• \(6\frac{4}{7}=\frac{6\times7+4}{7}=\frac{46}{7}\approx6.571\)
• \(9\frac{1}{7}=\frac{9\times7 + 1}{7}=\frac{64}{7}\approx9.142\)
• \(9\frac{3}{7}=\frac{9\times7+3}{7}=\frac{66}{7}\approx9.428\)

Since \(3\times\pi\approx9.428\), the closest is \(9\frac{3}{7}\)? Wait, no, wait, \(\pi\approx\frac{22}{7}\approx3.1429\), so \(3\times\pi\approx9.4287\). Now let's check the options:

\(9\frac{3}{7}=\frac{9\times7 + 3}{7}=\frac{66}{7}\approx9.4286\), which is very close to \(3\times\pi\). Wait, but let's re - check the calculation of \(3\times\frac{22}{7}\): \(3\times22 = 66\), so \(\frac{66}{7}=9\frac{3}{7}\) (because \(7\times9 = 63\), \(66-63 = 3\)). So the best estimate is \(9\frac{3}{7}\).

Wait, but let's check the options again. The options are \(6\frac{3}{7}\), \(6\frac{4}{7}\), \(9\frac{1}{7}\), \(9\frac{3}{7}\). Since \(3\times\pi\approx9.428\), and \(9\frac{3}{7}\approx9.428\), so that's the best estimate.

Answer:

\(9\frac{3}{7}\) (the last option)