Question

Convert 0.363636…10 to its exact equivalent base 8 numbe

Answer 1

Solution:

Consider the decimal number = 0.3636363636......₁₀

Convert to fractional part of decimal number to base-8 number.

F₁ = 0.3636363636 * 8 = 2.9090909090

(a₋₁) = 2

F₂ = 0.9090909090 * 8 = 7.272727272

(a₋₂) = 7

F₃ = 0.272727272 * 8 = 2.181818176

(a₋₃) = 2

F₄ = 0.181818176 * 8 = 1.454545408

(a₋₄) = 1

F₅ = 0.454545408 * 8 = 3.636363264

(a₋₅) = 3

F₆ = 0.636363264 * 8 = 5.090906112

(a₋₆) = 5

F₇ = 0.090906112 * 8 = 0.727248896

(a₋₇) = 0

F₈ = 0.727248896 * 8 = 5.817991168

(a₋₈) = 5

The base-8 equivalent number is:

F = [.(a₋₁, a₋₂, a₋₃, a₋₄, a₋₅, a₋₆, a₋₇, a₋₈)]

= [0.27213505...]₈

Hence, the base-8 equivalent number is [0.27213505...]₈.