Convert decimals and fractions to percents Write seller B's rating as a percent and a decimal. Given information: Customer satisfaction level of B as frac{3.5}{4}

Carol Gates 2021-01-19 Answered
Convert decimals and fractions to percents Write seller Bs
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Aniqa O'Neill
Answered 2021-01-20 Author has 100 answers
Calculation: Let us convert these into decimals and percent. For converting into a percent we multiply by 100 and then put per cent sign % 3.54=3.54(100)%
=3.5(25)%
=87.5% For decimal just divide percent by 100, i.e. shift the decimal point two digits to the left. 87.5%=87.5100
=0.875
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Definition 1:
Consider the measure space ( X , Σ , μ ).
A function f : X R is said to be measurable if, for every α R , { x X : f ( x ) > α } Σ.
The definition I knew was that

Definition 2 :
A function is measurable if the pre-image of every measurable set is measurable.
How come these definitions are equivalent?I suspect it has something to do with the fact that half-lines are generators of the Borel sigma algebra, but I haven't been able to prove it.
I guess the implication 2 -> 1 is trivial. If a function is measurable, half lines being borel sets, are measurable sets on R , therefore their preimages are measurable.
Can someone tell me if I am on the right track and complete the proof?