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HELP!!!!!!!!!!!!!!!!!!!!! Do all real numbers have a decimal expansion? Select each correct answer. Some numbers, such as 1 10 ​, have a decimal expansion that terminates. All real numbers have a decimal expansion. Some numbers, such as 13 − − √ , do not have a decimal expansion. Only some real numbers have a decimal expansion. Some numbers, such as 1 18 ​, have a decimal expansion that repeats but does not terminate.

Answer :

Answer:

1. Some numbers, such as [tex]\frac{1}{10}[/tex], have a decimal expansion that terminates.

2. All real numbers have a decimal expansion.

5. Some numbers, such as [tex]\frac{1}{18}[/tex], have a decimal expansion that repeats but does not terminate.

Step-by-step explanation:

According to the options, we have,

1. Some numbers, such as [tex]\frac{1}{10}[/tex], have a decimal expansion that terminates.

It is correct as the decimal expansion of [tex]\frac{1}{10}[/tex] is 0.1, which terminates.

2. All real numbers have a decimal expansion.

This is also correct as both rational and irrational numbers can be written in decimal form.

3. Some numbers, such as [tex]\sqrt{13}[/tex] do not have a decimal expansion

This is not correct as [tex]\sqrt{13}=3.605551275[/tex] i.e. it has a decimal expansion.

4. Only some real numbers have a decimal expansion.

It is not correct as 2 is correct.

5. Some numbers, such as [tex]\frac{1}{18}[/tex], have a decimal expansion that repeats but does not terminate.

It is correct as [tex]\frac{1}{18}=0.0555555..[/tex], which is non-terminating decimal expansion.

So, the correct options are,

1. Some numbers, such as [tex]\frac{1}{10}[/tex], have a decimal expansion that terminates.

2. All real numbers have a decimal expansion.

5. Some numbers, such as [tex]\frac{1}{18}[/tex], have a decimal expansion that repeats but does not terminate.

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