Lesson plan
Digital root
The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached. For example, in base 10, the digital root of the number 12345 is 6 because the sum of the digits in the number is 1 + 2 + 3 + 4 + 5 = 15, then the addition process is repeated for the resulting number 15, so that the sum of 1 + 5 equals 6, which is the digital root of that number. In base 10, this is equivalent to taking the remainder upon division by 9 (except when the digital root is 9, where the remainder upon division by 9 will be 0), which allows it to be used as a divisibility rule. The formula for the function \mathrm{dr}_b:\mathbb{N}\rightarrow\mathop{\bigcup}_{k=0}^{b-1}\{k\},\quad b\in\mathbb{N}_{\geqslant2} is expressed as: : \mathrm{dr}_b(n) := \begin{cases} 0 & n=0 \\ 1 + ((n - 1) \bmod (b - 1)) & n > 0\end{cases} .
Article summary
The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached. For example, in base 10, the digital root of the number 12345 is 6 because the sum of the digits in the number is 1 + 2 + 3 + 4 + 5 = 15, then the addition process is repeated for the resulting number 15, so that the sum of 1 + 5 equals 6, which is the digital root of that number. In base 10, this is equivalent to taking the remainder upon division by 9 (except when the digital root is 9, where the remainder upon division by 9 will be 0), which allows it to be used as a divisibility rule. The formula for the function \mathrm{dr}_b:\mathbb{N}\rightarrow\mathop{\bigcup}_{k=0}^{b-1}\{k\},\quad b\in\mathbb{N}_{\geqslant2} is expressed as: : \mathrm{dr}_b(n) := \begin{cases} 0 & n=0 \\ 1 + ((n - 1) \bmod (b - 1)) & n > 0\end{cases} .
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.