Question

Write each of the following numerals in base 10. For base​ twelve, T and E represent the face values ten and​ eleven, respectively.

a. 122 Subscript five
b. 11001 Subscript two
c. 16 Upper T Subscript twelve

Please show work!

Answer 1

a. 37

b. 25

c. 226

Explanation:

Place value has the same meaning in any other number base that it has in base 10. Using expanded form is one way to do the required base conversion.

a. 122₅ = 1×5² +2×5¹ +2×5⁰

= 25 +10 +2 = 37

__

b. 11001₂ = 1×2⁴ +1×2³ +0×2² +0×2¹ +1×2⁰

= 16 +8 + 1 = 25

__

c. 16T₁₂ = 1×12² +6×12¹ +10×12⁰

= 144 +72 +10 = 226