Name the sets of numbers to which each number belongs?

1) 6/7 is a rational number because it can be expressed as a ratio of two integers. Since all rational numbers are real numbers, 6/7 is also a real number.

3) 0 is a whole number and an integer. It is also a rational number (you could write 0 as 0/1) and a real number.

8) 26.1 is a rational number (you could write it as 261/10). Rational numbers can also be decimals that terminate, like this one.

14) $\sqrt{42}$ is an irrational number. It's decimal equivalent would be a non-repeating, non-terminating decimal. All square roots of positive integers that are not perfect squares are irrational numbers. The numbers $\pi$ and e are also irrational numbers. Since all irrational numbers are also real numbers, $\sqrt{42}$ is also a real number.

19) 894,000 is a natural number, a whole number, an integer, a rational number, and a real number.

A couple of other points:
- A number cannot be BOTH rational and irrational. It is one or the other.
- Note the hierarchy of these sets of numbers. Example: all integers are rational numbers, but not all rational numbers are integers.