Question

16 the circumferences of several circles are shown. \\(\frac{160}{7}\\), \\(7\pi\\), \\(20.2\\), \\(\frac{67}{3}\\) which shows the circumferences ordered from longest to shortest? a \\(\frac{160}{7}\\), \\(\frac{67}{3}\\), \\(20.2\\), \\(7\pi\\) b \\(\frac{67}{3}\\), \\(\frac{160}{7}\\), \\(7\pi\\), \\(20.2\\) c \\(20.2\\), \\(7\pi\\), \\(\frac{160}{7}\\), \\(\frac{67}{3}\\) d \\(\frac{160}{7}\\), \\(\frac{67}{3}\\), \\(7\pi\\), \\(20.2\\)

Explanation:

Step1: Calculate each value

First, calculate \(\frac{160}{7}\): \(\frac{160}{7}\approx22.86\) (divide 160 by 7).
Then, calculate \(7\pi\): \(7\pi\approx7\times3.14 = 21.98\) (use \(\pi\approx3.14\)).
We know \(20.2\) is already a decimal, and calculate \(\frac{67}{3}\): \(\frac{67}{3}\approx22.33\) (divide 67 by 3).

Step2: Compare the values

Now we have the approximate values:
\(\frac{160}{7}\approx22.86\), \(\frac{67}{3}\approx22.33\), \(7\pi\approx21.98\), \(20.2\).

Ordering from longest (largest) to shortest (smallest):
\(22.86\) (\(\frac{160}{7}\)) > \(22.33\) (\(\frac{67}{3}\)) > \(21.98\) (\(7\pi\)) > \(20.2\).

Answer:

D. \(\boldsymbol{\frac{160}{7}, \frac{67}{3}, 7\pi, 20.2}\)