How many numbers can you make with four digits?

Answer 1

Whole numbers . . .

All of the counting numbers from 1,000 to 9,999 = 9,000 of them.

Fractions . . .

-- all numerators from 1 to 9 / all denominators from 100 to 999 = 8,100

-- all numerators from 10 to 99 / all denominators from 10 to 99 = 8,100

-- all numerators from 100 to 999 / all denominators from 1 to 9 = 8,100

-- Total fractions = 24,300

Decimals . . .

-- All whole numbers from 1 to 9 plus all 3-place decimals from 0.100 to 0.999 = 8,100

-- All whole numbers from 10 to 99 plus all 2-place decimals from 0.10 to 0.99 = 8,100

-- All whole numbers from 100 to 999 plus all 1-place decimals from 0.1 to 0.9 = 8,100

-- Total decimals = 24,300

So far, we have a total of 57,600 numbers. But this is way off, for two reasons that I can think of just now:

1). I have not even considered mixed numbers ... combinations of a whole number and a fraction.

Including those would increase the total.

2). Many of the fractions, decimals, and whole numbers constructed in the above way

would be equal to each other.

So, that figure of 57,600 must be seen as a rough approximation of a ballpark

order-of-magnitude estimate. The refinement is left as an exercise for others,

because like a bad investment, I have lost interest.