This is a question about terminology when dealing with numbers, counting and incrementing digits.

In a decimal system we have 0-9 or 10 digits. Once we get past 9 we have to add a ? digit to get 10. (which means 1 set of 10 objects) Is 1 a leading digit? Does this have a name? And would it be correct to say it designates the magnitude?

What about the 0 in 10? Can the digits be referred to by specific terminology, does such a terminology exist?

Instinctively, I want to call this least/most significant, but that's used for something else. Front/end. Multiplier?

I'm trying to explain how numbers work and struggling to find the words to describe this. Essentially, when counting up and the last digit is passed, we append or increment the neighboring (left) digit.

Thanks, Paul

  • 1
    $\begingroup$ "Most significant digit" and "least significant digit" are exactly right for the first and last digit in a base $n$ expansion. Why do you think these terms mean something else? $\endgroup$ – Rob Arthan Mar 21 '16 at 23:19
  • $\begingroup$ Bah, I don't know why but I was conflating significant/non-significant with least/most! What a facepalm! $\endgroup$ – Paweł Czopowik Mar 21 '16 at 23:29

I would explain this using place value. These digits can be labeled as "units," "tens," "hundreds," "thousands," and so on from right to left. These labels are derived from the base-10 expansion of each number, as each place value is a number between 0-9 that designates how many of a certain power of 10 a number contains.

For example, the number $3284$ can be expressed as $3(10^3)+2(10^2)+8(10^1)+4(10^0)$, and this can demonstrate the relationship between each place value in the number $3284$.

  • $\begingroup$ That's exactly what I am explaining. It seems like place value is the correct terminology! $\endgroup$ – Paweł Czopowik Mar 21 '16 at 23:38

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