What is the best sequence of names to identify this set of numbers?

(1 3/5,-10, 0.51(the one is repeating), TT,17)
1.(rational,integer,irrational,irrational,natural)
2. (rational,irrational,rational, irrational, whole)
3.rational,real,rational,real, natural)
4. (real,integer, irrational,irrational,natural)

Off the bat I got rid of choices 2 and 3.
I picked choice#1 since a rational number is more specific and a real number can be rational or irrational.
Is this correct?
If I am not correct is there a website to hook me up with to explain the responses
Thank you

0.51111... is rational, as are all numbers with repeating decimal places. Its value is 0.5 + 1/90 = 23/45

so, the most specific ordering is

rational,integer,rational,irrational,natural

Looks to me like #3 is closest, since rational and irrational are mutually exclusive, and #1,2,4 all have "irrational" in a spot where the value is rational.

Based on the set of numbers provided, the best sequence of names to identify the numbers is:

4. (real, integer, irrational, irrational, natural)

In this option, the first number, 1 3/5, is a rational number since it can be expressed as a fraction. The second number, -10, is an integer. The third number, 0.51, is an irrational number since it contains a repeating decimal. The fourth number, TT, is not given a specific name, so it can be considered as either irrational or undefined. The fifth number, 17, is a natural number.

Your reasoning is correct in eliminating choices 2 and 3. Regarding choice 1, it is not accurate because not all real numbers are rational. Irrational numbers also fall under the category of real numbers. Therefore, choice 4 is the most appropriate sequence of names.

If you're looking for further information or resources to understand these concepts better, you can refer to math-related websites such as Khan Academy, Math is Fun, or Mathway. These platforms provide clear explanations and examples of different types of numbers and their classifications.

Based on the given set of numbers, the correct sequence of names to identify them is (rational, integer, irrational, irrational, natural).

You are correct in eliminating choices 2 and 3. Let's analyze the remaining options more closely:

1. (rational, integer, irrational, irrational, natural):
- 1 is a rational number because it can be expressed as the fraction 1/1.
- 3/5 is also a rational number.
- -10 is an integer because it is a negative whole number.
- 0.51 (repeating) is an irrational number because it is a non-terminating, non-repeating decimal.
- TT is not specified, so we cannot determine its category.
- 17 is a natural number because it is a positive whole number.

It's worth mentioning that TT could represent a variety of things since it is not specified. Without further information, it is unclear how to categorize it.

If you would like to further explore and understand the classification of numbers, you can refer to online resources such as math websites, educational resources, or even textbooks on number theory. Websites like Khan Academy, MathIsFun, and Mathplanet provide comprehensive explanations and examples regarding the classification of numbers.