What is the fewest number of distinct points that must be graphed on a number line, in order to represent natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers?

There are several types of numbers; and they are:

The fewest number of distinct points that must be graphed on a number line is 2.

In the above list:

Except irrational numbers, all other numbers are real numbers, and the relationship between them is as follows:

Real numbers Rational numbers Integers Whole numbers Natural numbers.

This means that 1 natural number can be used to represent the other numbers (real, rational, integer and whole numbers).

Similarly, 1 number can be used to represent the irrational numbers.

So, the fewest number (n) that can be used is:

n = 1 natural number + 1 irrational number

Hence, the fewest number of distinct points that must be graphed on a number line is 2.

Read more about numbers at:

link

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents