Evaluating (0.110 two)³ in base ten is (343/512) ten
The question has to do with number base
A number base is a system of numbering used to represent numbers.
Since we have (0.110 two)³,we desire to convert 0.110 two to base ten.
So, converting 0.110 two to base ten, following the procedure, we have that
0.110 two = 0 × 2⁰ + 1 × 2⁻¹ + 1 × 2⁻² + 1 × 2⁻³
= 0 × 2⁰ + 1 × 1/2¹ + 1 × 1/2² + 1 × 1/2³
= 0 × 1 + 1 × 1/2 + 1 × 1/4 + 1 × 1/8
= 0 + 1/2 +1/4 + 1/8
= (4 + 2 + 1)/8
= 7/8
So, thus 0.110 two = (7/8) ten
Thus we see that (0.110 two)³ = (7/8)³ ten
= (343/512) ten
So, expressing (0.110 two)³ in base ten is (343/512) ten
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