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Consider the following set:

[tex]\[ \left\{-4, 0, \frac{4}{5}, 0.\overline{4}, \sqrt{5}, \pi \right\} \][/tex]

Which are integers? Check all that apply:

[tex]\[\square\ -4\][/tex]
[tex]\[\square\ 0\][/tex]
[tex]\[\square\ \frac{4}{5}\][/tex]
[tex]\[\square\ 0.\overline{4}\][/tex]
[tex]\[\square\ \sqrt{5}\][/tex]
[tex]\[\square\ \pi\][/tex]

Sagot :

GinnyAnsweridn
To determine which numbers in the given set are integers, let's examine each one:

1. -4: This number is an integer because it is a whole number without any fractional or decimal component.
2. 0: This is also an integer, as it is a whole number and is explicitly defined as such in the set of integers.
3. [tex]\(\frac{4}{5}\)[/tex] (or 0.8): This is not an integer because it is a fraction and has a decimal component.
4. [tex]\(0.\overline{4}\)[/tex] (or 0.4444...): This is not an integer because it is a repeating decimal and not a whole number.
5. [tex]\(\sqrt{5}\)[/tex] (or the square root of 5): This is not an integer because the square root of 5 is an irrational number, approximately equal to 2.2360, and it has a non-terminating, non-repeating decimal portion.
6. [tex]\(\pi\)[/tex] (or pi, approximately 3.14159): This is not an integer because π is an irrational number and has a non-terminating, non-repeating decimal expansion.

After analyzing each number in the set, we conclude that the integers in the given set are:

- -4
- 0

Thus, the integers in the set are:

[tex]\[ \{-4, 0\} \][/tex]
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