Is 0.123 a three-digit or four-digit number?
A four digit number implies that the the four places to the left of the decimal point are occupied.
It is a decimal fraction taken to three decimal places.
After my initial post, I researched this question a bit and did find some support for my answer.
But first, I don't disagree with what David said, in that a 'four digit number' does usually imply a whole number between 1,000 and 9,999. If someone says 'the number of people there was well into 4 digits', it means there were considerably more than 1,000 people there.
And it's also true that "0.123" is a decimal fraction, which is defined by ThefreeDictionary as "a decimal having no digits to the left of the decimal point except zero". (my underlining)
And the digits to the right of the decimal point are called decimal digits. (defined as 'a digit from 0 to 9 in decimal rotation')
So from the above perspective, the number ".123" has 3 (decimal) digits, and, also following from the above, the number "0.123" would have 4 digits. (the zero to the left and the 3 decimal digits)
Now one can say that the above zero is unnecessary, but it is very commonly included to the left of the decimal point in decimal fractions and is described as a digit in the above definitions.
So maybe '4 digits' is the correct answer, but the final word can rest with an appropriate mathematics expert. Any volunteers?