Convert Base 7 to Decimal

Convert Base 7 (base 7) to Decimal (dec) instantly and accurately.

Selected Base 7 (base 7) - available characters: 0, 1, 2, 3, 4, 5, 6

Conversion Formula

Step-by-step example using the value 42 (decimal):

Convert Base 7 (base 7) → Decimal (base 10)

Step 1: Expand each digit of 60 (base 7) by position:

        6 × 7^1 = 42
        0 × 7^0 =  0
        ────────────
        Sum = 42 (decimal)

Step 2: Target is decimal - Step 1 result is the final answer.

────────────────────────────
Result:  60 (base 7) = 42 (dec)

About Base 7

Septenary (base 7) uses digits 0-6. Each position is a power of 7: 7⁰=1, 7¹=7, 7²=49. Seven is prime, so every fraction p/q (q not divisible by 7) produces a purely repeating expansion. Seven days of the week derive from Babylonian astronomy (the 7 naked-eye celestial objects). Reed-Solomon codes used in QR codes and Blu-ray draw on prime-field properties of GF(7). Conversion: decimal 42 = 6×7+0 = 60₇.

About Decimal

Decimal (base 10) is the universal positional system using digits 0-9. Each position is a power of 10: 10⁰=1, 10¹=10, 10²=100. Attributed to human anatomy (ten fingers). The Hindu-Arabic system - including zero - was formalised by Brahmagupta (628 CE) and spread via al-Khwarizmi (c. 820 CE). SI and metric systems are base-10. IEEE 754-2008 added decimal64/128 formats for exact decimal arithmetic in financial applications. Conversion: decimal 42 is the reference value used throughout this converter.

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