Convert Decimal to Base 7

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

Selected Decimal (dec) - available characters: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Conversion Formula

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

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

Step 1: Input is already decimal - skip to Step 2.
        Value: 42

Step 2: Divide 42 by 7 repeatedly (read remainders upward):

        42 ÷ 7 = 6  r 0
         6 ÷ 7 = 0  r 6
        Read remainders upward: 60

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

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.

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.

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