Four people have found the distance in kilometers across a small bridge using different methods.

Question

Their results are given in the table. Order the distances from least to greatest.
5.555555... 23/4 28sqared 5(1/2

(1 point)
Responses

512, 28−−√, 5.5¯¯¯, 234
512, 28−−√, 5.5¯¯¯, 234

28−−√, 512, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 234

28−−√, 5.5¯¯¯, 234, 512
28−−√, 5.5¯¯¯, 234, 512

234 , 5.5¯¯¯, 28−−√, 512

Answer 1

First, let’s convert all the values to numerical form so we can compare them easily.

1. 5.555555... = \(5.\overline{5}\) = \(5.5\) (since it is a repeating decimal).

2. 23/4 = \(5.75\) (since \(23 ÷ 4 = 5.75\)).

3. 28\(\sqrt{}\) = \(28^{1/2}\) = \( \sqrt{28} \approx 5.2915\) (since \(\sqrt{28}\) is approximately \(5.2915\)).

4. 5(1/2) = \(5.5\) (interpreted as \(5 + \frac{1}{2}\) = \(5.5\)).

Now let's summarize the numerical values:

• \( \sqrt{28} \approx 5.2915\)
• \( 5.555555... = 5.5\) (two instances)
• \( 5.75\) (which is \(23/4\))

Now, we have:

• \( \sqrt{28} \approx 5.2915 \)
• \( 5.5 \)
• \( 5.5 \)
• \( 5.75 \)

Ordering these from least to greatest:

1. \( \sqrt{28} \approx 5.2915 \)
2. \( 5.5 \)
3. \( 5.5 \)
4. \( 5.75 \)

So the ordered distances from least to greatest are: \[ \sqrt{28}, 5.5, 5.5, 5.75 \]

Thus, the correct response would be: √28, 5.5, 23/4, 5.5 in terms of their respective numerical order. However, we also have 23/4 (which is 5.75, but is equivalent to the last 5.5). So, it is more succinctly as:

√28, 5.5, 5.75.