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

Answer:

1. Some numbers, such as $\frac{1}{10}$, have a decimal expansion that terminates.

2. All real numbers have a decimal expansion.

5. Some numbers, such as $\frac{1}{18}$, 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 $\frac{1}{10}$, have a decimal expansion that terminates.

It is correct as the decimal expansion of $\frac{1}{10}$ 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 $\sqrt{13}$ do not have a decimal expansion

This is not correct as $\sqrt{13}=3.605551275$ 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 $\frac{1}{18}$, have a decimal expansion that repeats but does not terminate.

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

So, the correct options are,

1. Some numbers, such as $\frac{1}{10}$, have a decimal expansion that terminates.

2. All real numbers have a decimal expansion.

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