Question

To which subset of the real number system does the number 1.5¯(repeating decimal)  belong to?

A.

whole numbers

B.

natural numbers

C.

rational numbers

D.

irrational numbers

Answer 1

Here we have the number 1.555...

We want to find to which set this number belongs.

We will find that this is a rational number (like all of these with repeating decimals), let's see that:

First, remember that the whole numbers and natural numbers do not have any digit after the decimal point, so we can already discard these options.

Now, the rational numbers are the ones that can be written as the quotient of two whole numbers, while the irrationals are the ones that can't

So let's try to write our number as the quotient of two whole numbers.

N = 1.555...

First, let's multiply it by 10 (equal number of zeros as the repeating digits after the decimal point, here the only digit that repeats is the 5, so we use only one zero)

1.555...*10 = 15.555...

now we can subtract the original number:

1.555...*10 - 1.555... = 1.555....*9 = 15.555... - 1.555... = 14

Then we have:

1.555....*9 = 14

Solving for our number, we get:

1.555... = 14/9

So we wrote our number as the quotient of two whole numbers, which means that our number is a rational number.

If you want to learn more, you can read:

https://brainly.com/question/12542057

Answer 2

Using number sets, it is found that the number belong to the set of rational numbers, given by option C.

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The numbers may be classified as:

• Whole: All positive non-decimal numbers and 0, so: {0,1,2,...}
• Integer: Whole plus negatives.
• Rational: Integer plus decimals that can be represented by fractions, that is, they either have a pattern, or have a finite number of decimal digits
• Irrational: Non-repeating decimals.
• Real: Rational plus irrational.

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Repeating decimals, such as 1.5¯ = 1.555555555..., are rational, thus the correct option is C.

A similar problem is given at https://brainly.com/question/10814303