# How do you order the rational numbers from least to greatest: -4 3/5 -3 2/5, -4.65, -4.09?

Order from least to greatest is

When all numbers are negative, the number having greatest numerical value is least and number having least numerical value is greatest.

But for that it is always preferable to write all the numbers up to a reasonable number of decimal places for comparing them, let us say three here.

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Notice that the fractions are in 5ths and that the smallest decimal part in 100ths. It is relatively straightforward to change these all into the same units for direct comparison.

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To order the given rational numbers from least to greatest, follow these steps:

- Convert mixed numbers to improper fractions if needed.
- Compare and order the numbers.

Given numbers:

- ( -4 \frac{3}{5} ) can be converted to an improper fraction as ( -\frac{23}{5} ).
- ( -3 \frac{2}{5} ) can be converted to an improper fraction as ( -\frac{17}{5} ).

Now, the list of numbers becomes:

- ( -\frac{23}{5} )
- ( -\frac{17}{5} )
- ( -4.65 )
- ( -4.09 )

To order them from least to greatest:

- ( -\frac{23}{5} ) (which is ( -4 \frac{3}{5} ))
- ( -\frac{17}{5} ) (which is ( -3 \frac{2}{5} ))
- ( -4.65 )
- ( -4.09 )

So, the rational numbers ordered from least to greatest are: [ -\frac{23}{5}, -\frac{17}{5}, -4.65, -4.09 ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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