Calculate 3310base 5 - 1442base 5

Answer 1

It’s base number problem.

 First convert base 5 to base 10.

 3310₅ = (3 · 5³+ 3 · 5²+ 1 · 5¹ + 0  · 5⁰)₁₀ = 455₁₀

 1442₅ = (1 · 5³+ 4 · 5²+ 4 · 5¹ + 2  · 5⁰)₁₀ = 247₁₀

 3310₅ -  1442₅ =  455₁₀  - 247₁₀ = 208₁₀

 Next Convert base 208 base 10 into base 5.

 208 = a₀ + 5a₁ + 25a₂ + 125 a₃ + 625 a₄ + 3125a₅.

where all the are a_i digits from 0 to 4. Obviously, all the a_i from a₄ and up  are 0 since otherwise they will add in a number greater than 208, and all the terms in the sum are nonnegative. Then, we wish to find the largest a₃ such that 125a₃ does not exceed 208. Thus, a₃ = 1 since 1a₃ = 125 and 2a₃ = 250.

 This leaves us with 208 = a₀ + 5a₁ + 25a₂ + 125(1) à 83 = a₀ + 5a₁ + 25a₂

 83 = a₀ + 5a₁ + 25(3)à 8 = a₀ + 5a₁

 8 = a₀ + 5 (1) à a₀ = 3

 a₀  = 3, a₁  = 1, a₂  = 3 and a₃ = 1

 208 ₁₀= 1313₅.

 Let's check by converting answer back into base 10. We know that

 1313₅ = (1 · 5³+ 3 · 5²+ 1 · 5¹ + 3 · 5⁰)₁₀ = 125 + 75 + 5 + 3 = 208.

 

3310₅  - 1442₅ = 208 ₁₀= 1313₅.

I hope it helps a lil.