High School

Sort these numbers:

[tex]\frac{9}{10}, 0.85, \frac{4}{5}, \frac{18}{20}, \frac{6}{10}, 0.72, \frac{1}{2}, \frac{20}{25}[/tex]

Answer :

To sort the given numbers, we first need to understand what each number represents as a decimal. This makes it easier to arrange them in order. Let's break it down step by step.

1. Convert all fractions to decimals:
- [tex]\(\frac{9}{10} = 0.9\)[/tex]
- [tex]\(\frac{4}{5} = 0.8\)[/tex]
- [tex]\(\frac{18}{20} = 0.9\)[/tex]
- [tex]\(\frac{6}{10} = 0.6\)[/tex]
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
- [tex]\(\frac{20}{25} = 0.8\)[/tex]

2. List all given numbers with their decimal equivalents:
- [tex]\(0.9\)[/tex] (from [tex]\(\frac{9}{10}\)[/tex])
- [tex]\(0.85\)[/tex] (already a decimal)
- [tex]\(0.8\)[/tex] (from [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{20}{25}\)[/tex])
- [tex]\(0.9\)[/tex] (from [tex]\(\frac{18}{20}\)[/tex])
- [tex]\(0.6\)[/tex] (from [tex]\(\frac{6}{10}\)[/tex])
- [tex]\(0.72\)[/tex] (already a decimal)
- [tex]\(0.5\)[/tex] (from [tex]\(\frac{1}{2}\)[/tex])

3. Sort the decimal values from smallest to largest:
- [tex]\(0.5\)[/tex]
- [tex]\(0.6\)[/tex]
- [tex]\(0.72\)[/tex]
- [tex]\(0.8\)[/tex]
- [tex]\(0.8\)[/tex]
- [tex]\(0.85\)[/tex]
- [tex]\(0.9\)[/tex]
- [tex]\(0.9\)[/tex]

So, the sorted numbers from smallest to largest are:
[tex]\[ 0.5, 0.6, 0.72, 0.8, 0.8, 0.85, 0.9, 0.9 \][/tex]

This is the order when each number is represented as a decimal.

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