Question

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 1

1. Some numbers, such as
`(1)/(10)`, have a decimal expansion that terminates.

2. All real numbers have a decimal expansion.

5. Some numbers, such as
`(1)/(18)`, have a decimal expansion that repeats but does not terminate.

Explanation:

According to the options, we have,

1. Some numbers, such as
`(1)/(10)`, have a decimal expansion that terminates.

It is correct as the decimal expansion of
`(1)/(10)` 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
`√(13)` do not have a decimal expansion

This is not correct as
`√(13)=3.605551275` 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
`(1)/(18)`, have a decimal expansion that repeats but does not terminate.

It is correct as
`(1)/(18)=0.0555555..`, which is non-terminating decimal expansion.

So, the correct options are,

1. Some numbers, such as
`(1)/(10)`, have a decimal expansion that terminates.

2. All real numbers have a decimal expansion.

5. Some numbers, such as
`(1)/(18)`, have a decimal expansion that repeats but does not terminate.