Sūtra 12 of 16
Śeṣāṇyaṅkena Carameṇa
The remainders by the last digit
Computing recurring decimals of fractions like 1/7.
When to use
Long division producing recurring decimals.
How it works
After dividing, the digit obtained at each step is the next decimal; the remainder times the next digit pattern continues the cycle.
Memory formula
Track each remainder; the recurring decimal cycle repeats when the remainder repeats.
Worked examples
Problem 1
1/7 as a decimal
0/7
Modern applications
Where this ancient technique still lives in today's world.
Coding
Periodic decimals
Detecting recurring decimals = detecting cycles in modular arithmetic — used in primality testing (Pollard's rho) and PRNG design.
Stuck? Ask the tutor.
Get a personal walkthrough of Śeṣāṇyaṅkena Carameṇa with examples tuned to your question.
Open AI Tutor