Geometry Basics (G8)
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Convert to base 10: 133₅ = 1×25 + 3×5 + 3 = 25+15+3=43₁₀. 43₅ = 4×5 + 3 = 23₁₀. Product = 43 × 23 = 989₁₀. Convert back to base 5: 5³=125, 5⁴=625. 989 ÷ 625 = 1 remainder 364; 364 ÷ 125 = 2 remainder 114; 114 ÷ 25 = 4 remainder 14; 14 ÷ 5 = 2 remainder 4. So digits: 1,2,4,2,4 => 12424₅. Check: 133₅ × 43₅. Let's multiply in base 5: 133 × 40 = (133 × 4) × 10₅ = ( (1×4=4, 3×4=12->carry, etc) ) Actually easier to do base 10. 989₁₀ in base 5: 5⁴=625, 5³=125, 5²=25, 5¹=5, 5⁰=1. 989 = 625*1=625 remainder 364; 125*2=250 remainder 114; 25*4=100 remainder 14; 5*2=10 remainder 4; units 4. So 12424₅. Correct.
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