Jadhav Division Axiom

From ProofWiki
Jump to navigation Jump to search

Jadhav Division Axiom, gives a way to correctly predict the number of digits before decimal point in an incomplete or improper, division process left with remainder zero and a Quotient with decimal part, given by Jyotiraditya Jadhav

Statement

In an incomplete division process if the dividend is lesser then Divisor into product of 10 raise to a power "k", and bigger then divisor into product of 10 with power "k-1" then there will be k number of terms before decimal point in an divisional process.

\(d \times 10^k-1<n < d \times 10^k \)

Number of digits before decimal point is k (here d represents divisor and n represents dividend)

Practical Observations

22/7 = 3.14

here { 7 X 10 ^(1-1) < 22 < 7 X 10^1 } , so number of digits before decimal point is 1

100/ 6 = 16.6

here {6 X 10^(2-1)<100<6 X 10^2 }, so number of digits before decimal point is 2

Uses

  • All type of division processes
  • Can be used to correctly predict the nature of the answer for long division processes.
  • Can be used to determine the sin and cosine functions of extreme angles[1]

Sources