Function to grab specific digits from a number?Recently I’ve been thinking a lot about grabbing digits from numbers, for things like calculating multiplication persistence, i.e. turning&nbsp;1234&nbsp;into a&nbsp;1×2×2×3×4. I’ve been able to come up with[log⁡x]+1to output the number of digits of the given number x, as well as⌊x10⌊log⁡x⌋−n+1⌋which outputs the first n digits of any number x. But that’s about as far as I’ve been able to think up. Is there any way to construct a function that retrieves the nth digit of a given number? Forgive me if my notation or comprehension is poor, I have no formal education in this field of maths.

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Function to grab specific digits from a number?Recently I’ve been thinking a lot about grabbing digits from numbers, for things like calculating multiplication persistence, i.e. turning&amp;nbsp;1234&amp;nbsp;into a&amp;nbsp;1×2×2×3×4. I’ve been able to come up with[log⁡x]+1to output the number of digits of the given number x, as well as⌊x10⌊log⁡x⌋−n+1⌋which outputs the first n digits of any number x. But that’s about as far as I’ve been able to think up. Is there any way to construct a function that retrieves the nth digit of a given number? Forgive me if my notation or comprehension is poor, I have no formal education in this field of maths.

Theodore Davila · Accepted Answer

Step 1If the digit you require is n places from the right (indexed from zero so the units place is at position 0, the tens place is at 1 and so forth), then the following function will return the n-th digit of the decimal integer x:f(x,n)=⌊x10n⌋(mod10)Example:&amp;nbsp;f(123456,3)=3You can replace 10 everywhere in the formula with any base b to generalise it.

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