Bidirectional conversion between vigesimal (base 20) and decimal with detailed steps
Input Value
Result
Conversion Result
Step-by-Step Derivation
Base Conversion Principle
Vigesimal → Decimal: Place value expansion (each digit × 20ⁿ) and sum
Decimal → Vigesimal: Repeated division by 20 (reverse remainders)
Digits: 0-9, A=10, B=11, ..., J=19
Vigesimal (base 20) is a positional numeral system with twenty as its base. It was used by the Maya civilization and appears in some traditional counting systems, with natural divisibility by 2, 4, 5, and 10.
⚠Vigesimal numbers use digits 0-9 and letters A-J (uppercase). A=10, B=11, C=12, D=13, E=14, F=15, G=16, H=17, I=18, J=19. Any digit beyond J is invalid in base 20.
What Is Vigesimal (Base 20)?
Vigesimal is a base-20 number system. It uses twenty digits: 0-9 and A-J, where A=10, B=11, C=12, D=13, E=14, F=15, G=16, H=17, I=18, and J=19. The Maya civilization used a sophisticated vigesimal system for their calendar and astronomical calculations.
Historical Significance
The Maya used a vigesimal system with a symbol for zero. They counted in 20s, with special notations for their Long Count calendar and astronomical observations.
Place Value Expansion
Vigesimal to decimal: multiply each digit by 20^position. For example, 1A8₂₀ = 1×400+10×20+8×1 = 608₁₀.
Repeated Division by 20
Decimal to vigesimal: repeatedly divide by 20, collect remainders, and read in reverse. Remainders 10-19 become A-J.
Modern Residues
Vigesimal traces remain in French (quatre-vingt = 80), Danish (tre-sindstyve = 60), and Welsh counting systems, showing historical vigesimal usage.
💡 Teaching Example: Convert vigesimal 1A8₂₀ to decimal. Place value expansion: 1×20²+10×20¹+8×20⁰ = 1×400+10×20+8×1 = 400+200+8 = 608₁₀. Conversely, 608₁₀: 608÷20=30 r8, 30÷20=1 rA, 1÷20=0 r1 → 1A8₂₀.
Vigesimal is a base-20 number system using digits 0-9 and A-J (representing 10-19). It is historically used by the Maya civilization and in some traditional counting systems, with a convenient division by 2, 4, 5, and 10.
How do you convert vigesimal to decimal?▼
Place value expansion: multiply each vigesimal digit by its power of 20, then sum. For example, 1A8₂₀ = 1×20²+10×20¹+8×20⁰ = 1×400+10×20+8×1 = 400+200+8 = 608₁₀.
How do you convert decimal to vigesimal?▼
Repeated division by 20: repeatedly divide by 20, collecting remainders. Remainders 10-19 become A-J. Read remainders in reverse. For example, 608÷20=30 r8, 30÷20=1 rA, 1÷20=0 r1 → 1A8₂₀.
What is the historical significance of base 20?▼
The Maya civilization used a sophisticated vigesimal system for astronomy and calendar calculations. Base 20 may have originated from counting fingers and toes (10 fingers + 10 toes = 20). It also appears in French counting (quatre-vingt = four-twenty = 80).
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