Number times Recurring Part of Reciprocal gives 9-Repdigit/Examples/37

Example of Use of Number times Recurring Part of Reciprocal gives 9-Repdigit

\(\ds \dfrac 1 {37}\)

\(=\)

\(\ds 0 \cdotp \dot 0 2 \dot 7\)

\(\ds 27 \times 37\)

\(=\)

\(\ds 10^3 - 1\)

Proof

Let $x = \dfrac 1 {37} = 0 \cdotp \dot 0 2 \dot 7$.

Then $n = 37$; $m = 27$ and $d = 3$

Therefore:

$27 \times 37 = 10^3 - 1$

$\blacksquare$