Question

order these numbers from least to greatest.
\\(\frac{77}{20}\\), \\(3\frac{10}{11}\\), 3.82, 3.815
\\(\frac{77}{20}\\) \\(3\frac{10}{11}\\) 3.82 3.815
\\(\square\\) < \\(\square\\) < \\(\square\\) < \\(\square\\)

Explanation:

Step1: Convert fractions to decimals

$\frac{77}{20} = 3.85$, $3\frac{10}{11} \approx 3.909$

Step2: List all decimal values

$3.85$, $3.909$, $3.82$, $3.815$

Step3: Compare and order from least to greatest

Compare each decimal digit by digit starting from the ones place:
$3.815 < 3.82 < 3.85 < 3.909$

Step4: Replace decimals with original values

Map the ordered decimals back to their original fraction/number forms.

Answer:

$3.815 < 3.82 < \frac{77}{20} < 3\frac{10}{11}$