Question

order these numbers from least to greatest.
5.12, 5.831, \\(\frac{117}{20}\\), \\(5\frac{5}{6}\\)
5.12 5.831 \\(\frac{117}{20}\\) \\(5\frac{5}{6}\\)
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Explanation:

Step1: Convert fractions to decimals

First, convert \(\frac{117}{20}\) to decimal. \(\frac{117}{20}=117\div20 = 5.85\). Then, convert \(5\frac{5}{6}\) to decimal. \(5\frac{5}{6}=\frac{35}{6}\approx5.833\) (since \(35\div6\approx5.833\)).

Step2: Compare the decimals

Now we have the numbers as decimals: \(5.12\), \(5.831\), \(5.85\), and \(5.833\). Comparing these decimals: \(5.12\) is the smallest. Then, \(5.831\) is next (since \(5.831<5.833\)). Then \(5\frac{5}{6}\approx5.833\), and the largest is \(\frac{117}{20} = 5.85\). So the order from least to greatest is \(5.12\), \(5.831\), \(5\frac{5}{6}\), \(\frac{117}{20}\).

Answer:

\(5.12 < 5.831 < 5\frac{5}{6} < \frac{117}{20}\)