Question

MATHEMATICS Evaluate (0.110 two)³ expressing your answer in base ten.

Answer 1

Evaluating (0.110 two)³ in base ten is  (343/512) ten

The question has to do with number base

What is number base?

A number base is a system of numbering used to represent numbers.

How to evaluate  (0.110 two)³ in base ten.

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

Learn more about number base here:

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