How this instrument works
Place value describes what a single digit is worth by virtue of where it sits, and this sheet isolates exactly one of those contributions rather than unpacking the whole number at once. The formula does the isolating in two moves: dividing x by 10 raised to the position pushes the digit you want down into the ones column, and flooring that quotient discards every digit sitting to its right. The mod 10 that follows then discards everything to its left, since two numbers differing only past the tens place agree with each other modulo ten. What survives both operations is the single digit you asked for, cut cleanly away from its neighbors on either side.
Position counts rightward from the decimal point, starting at zero, so position 0 names the ones digit (10⁰ = 1), position 1 names the tens digit (10¹ = 10), and so on — the position number and the exponent it feeds into are always the same integer, which is less a coincidence than the actual definition of positional notation. A sibling sheet on this site, expanded form, breaks a number into every place value at once and adds them back together; this one answers a narrower question — what does just the hundreds digit, or just the ten-thousands digit, contribute on its own — the kind of single-field lookup you need when checking one part of an account number or a serial code rather than reconstructing the whole thing.
Ask for a position beyond the number's leading digit and both outputs settle on zero without complaint: position 6 applied to 4,832 returns digit 0 and value 0, since flooring has already passed every digit the number actually owns before the mod 10 even runs. The formula only means something for whole-number positions counting up from zero — it has no notion of position −1 or of a digit sitting after a decimal point, because floor division and remainder are both integer operations from the start.
- Type the number you're inspecting into the Number field.
- Set Digit position (0 = ones, 1 = tens, 2 = hundreds, …) to the place you're targeting, counting rightward from zero.
- Read Digit at that position for the single digit sitting there.
- Read Place value (digit × 10^position) for what that digit is actually contributing to the number as a whole.
Worked example — the hundreds digit of 4,832
Set x = 4,832 and position = 2, targeting the hundreds place. First, floor(4832 ⁄ 10²) = floor(4832 ⁄ 100) = floor(48.32) = 48 — the division has pushed the hundreds digit down into the ones column, along with everything above it. Next, 48 mod 10 = 8, which strips away the tens and thousands that came along for the ride, leaving digit = 8. That matches what you'd read straight off the numeral: 4,832 has an 8 sitting in the hundreds place.
Place value then just multiplies that digit back by its position's power of ten: value = 8 × 10² = 8 × 100 = 800. So the hundreds digit of 4,832 is 8, and it is worth 800 toward the total — a single term isolated on its own, with no need to work out what the thousands, tens, or ones digits are contributing.
Questions
What does the digit position number actually mean?
It's the exponent of ten attached to that place, counted from the right starting at zero: position 0 is ones (10⁰), position 1 is tens (10¹), position 2 is hundreds (10²), and so on. It is not the digit's position counted from the left of the numeral, which is the opposite direction and depends on how many digits the number has.
Why does the formula use floor division and then mod 10?
Floor division by 10^position shifts the target digit into the ones column and drops every digit below it; mod 10 then removes everything above it, since numbers agree modulo ten once you ignore all digits past the tens place. Together the two steps leave only the one digit you asked for.
How is this different from the expanded form calculator?
Expanded form decomposes a whole number into all of its place values simultaneously and adds them back together to confirm nothing was lost. This sheet answers a narrower question — the digit and value at one chosen position only — useful for spot-checking a single field of a number rather than reconstructing it entirely.
What happens if the position is larger than the number has digits?
Both outputs come back 0. Ask for position 6 on 4,832, which only has four digits, and floor(4832 ⁄ 10⁶) already rounds down to 0 before the mod 10 step even runs, so digit = 0 and value = 0 — there is simply nothing occupying that place.
Can position be negative to reach digits after a decimal point?
No — this formula is built from integer floor division and remainder, which only have a defined meaning for whole-number positions counting up from zero. Extracting a digit after a decimal point needs a different construction, since 10^position would have to be a fraction rather than a whole power of ten.
Does the digit at a position ever differ from what I'd read by eye?
No — for any valid whole-number input the formula always reproduces exactly the digit printed in that place, since floor division and mod 10 are just arithmetic descriptions of the same base-ten place-value system used to write the numeral in the first place. The two never disagree.