Reciprocal of Square of 1 Less than Number Base/Examples/6

Example of Reciprocal of Square of 1 Less than Number Base

Expressed in base $6$, the reciprocal of $5^2$ has the expansion:

$\dfrac 1 {5^2} = \sqbrk {0 \cdotp \dot 0123 \dot 5}_6$

Proof

From Square of $1$ Less than Number Base: $5$ we have:

$5^2 = 41_6$

Performing the calculation using long division:

   0.0123501...
  ----------------
41)1.0000000000
     41
     --
     150
     122
     ---
      240
      203
      ---
       330
       325
       ---
         100
          41
          --
         ...

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $81$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $81$