Convert an octal number with a fractional part (such as 7.4) to decimal exactly – digits after the point use negative powers of 8.
Show calculation steps
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Eighths after the point
Fractional octal places weigh 1/8, 1/64, 1/512 — negative powers of eight. Summing the weighted digits gives the decimal value, always exactly: since 8 is 2³ and 2 divides 10, every finite octal fraction terminates in decimal, needing at most three decimal digits per octal place.
The rarity of octal fractions today makes them a favourite exam topic — and an occasional reality in vintage-format archaeology.
Worked example
Input: 7.4 Integer: 7 Fraction: 4/8 = 0.5 Result: 7.5 (exact)
Place weights
| Place | Weight |
|---|---|
| .1 | 1/8 = 0.125 |
| .4 | 4/8 = 0.5 |
| .01 | 1/64 ≈ 0.0156 |
| .44 | 4/8 + 4/64 = 0.5625 |
Historical footing
Machines with 12-, 24- and 36-bit words — the PDP-8 lineage among them — documented everything in octal, fractions included: scaling factors, fixed-point constants, device registers. Reading those manuals today means reading octal fractions; this page is the bridge back.
Guarantees and privacy
Exact rational evaluation with positional digit validation — 8s and 9s rejected by name. Single point enforced. Conversion runs locally; nothing about your values is retained.
Reading digits after the octal point
Digits after the point in octal follow the same positional rule as the integer side, with the column values continuing downward through the negative powers of eight: 1/8, 1/64, 1/512. So 0.4₈ is 4/8 = 0.5, 0.2₈ is 0.25, and 7.4₈ is exactly 7.5. Because this converter uses exact fraction arithmetic, values that cannot terminate come back with their true repeating cycle: one third, for example, is 0.252525… in octal, repeating “25” forever, and the tool marks that cycle rather than rounding it away.
How to use the Octal Fraction to Decimal Converter
- Enter an octal value with a point, such as 7.4.
- Click "Convert to decimal".
- The steps use negative powers of 8 – 1/8, 1/64 – for the digits after the point.
- The result is exact; octal fractions always terminate in decimal.
Frequently asked questions
What is the place value after the octal point?
Eighths, then sixty-fourths: .4 is 4/8 = one half, so 7.4 octal = 7.5 decimal. Each further place divides by 8 again.
Why is the decimal expansion always finite?
Because 8 = 2³ and 2 divides 10 – the same reason binary and hex fractions terminate in decimal. n octal places need at most 3n decimal places.
Where would I meet an octal fraction?
Historic computing documentation (PDP-era word formats), some avionics and legacy protocol specs, and coursework – it is rarer than hex today but identical in principle.
Is .4 octal the same as .5 decimal – why?
Yes: 4/8 reduces to 1/2. Different digits, same quantity – a compact demonstration that the digits depend on the base, the value does not.
What inputs fail?
Digits 8 or 9 anywhere (named with position), or two points. Valid input cannot overflow – the fraction arithmetic is unbounded and exact.
Can I go the other way?
The Decimal Fraction to Octal converter is the exact inverse, including repeat detection for values that have no finite octal form.
Local processing again?
Yes – the rational arithmetic runs in the page. Your value is never sent anywhere.
