Question

Four people have found the distance in kilometers across a small bridge using different methods. Their results are given in the table. Order the distances from least to greatest. (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

To order the distances from least to greatest, we first need to evaluate each of the values provided:

1. **512 km** - This is already a clear number, so we keep it as is.

2. **√28 km** - Calculating this using a calculator or estimating:
- √28 = √(4*7) = 2√7 ≈ 2 * 2.64575 = 5.291.
So, √28 ≈ 5.291 km.

3. **5.5̅ km (often written as \( \frac{5}{9} \) or repeated decimals)** - This notation means that 5.5 repeats indefinitely, which is approximately 5.555... km, more exactly it is \( \frac{50}{9} \) which is around 5.555... km.

4. **234 km** - This is also a clear number.

Now we can summarize the values we've computed:
- \( √28 ≈ 5.291 \) km
- \( 5.5̅ ≈ 5.555\) km
- 234 km
- 512 km

Now, let's compare them:
1. **√28 ≈ 5.291** km
2. **5.5̅ ≈ 5.555** km
3. 234 km
4. 512 km

Ordering these from least to greatest:
1. √28
2. 5.5̅
3. 234
4. 512

So, the order from least to greatest is:
√28, 5.5̅, 234, 512.