Question

Write 16.2 ten as a base five numeral

Answer 1

I assume you're asked to convert 16.2 from base 10 to base 5. We have

16.2₁₀ = 1•10¹ + 6•10⁰ + 2•10⁻¹

Since 10 = 2•5, we can expand this as

16.2₁₀ = 1•(2•5)¹ + 6•(2•5)⁰ + 2•(2•5)⁻¹

16.2₁₀ = 2•5¹ + 6•5⁰ + 1•5⁻¹

Next, 6 = 5 + 1, so

16.2₁₀ = 2•5¹ + (5 + 1)•5⁰ + 1•5⁻¹

16.2₁₀ = 2•5¹ + 1•5¹ + 1•5⁰ + 1•5⁻¹

16.2₁₀ = 3•5¹ + 1•5⁰ + 1•5⁻¹

16.2₁₀ = 31.1₅