Four Fifths as Pandigital Fraction

Theorem

The fraction $\dfrac 4 5$ can be expressed as a pandigital fraction in the following interesting way:

$\dfrac 4 5 = \dfrac {9876} {12 \, 345}$

Proof

Can be found by brute force.

Also see

• One Half as Pandigital Fraction
• One Third as Pandigital Fraction
• One Quarter as Pandigital Fraction
• One Fifth as Pandigital Fraction
• One Sixth as Pandigital Fraction
• One Seventh as Pandigital Fraction
• One Eighth as Pandigital Fraction
• One Ninth as Pandigital Fraction

Historical Note

According to David Wells in his $1986$ work Curious and Interesting Numbers, this result may have appeared in an article by Mitchell J. Friedman in Volume $8$ of Scripta Mathematica, but it is proving difficult to find an archived copy to consult directly.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $0 \cdotp 5$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $0 \cdotp 5$