What is 305 divided by 1000?
2 answers:
Answer: 0.305 ; or, as fraction: 
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Note: 305/1000 would be 305 ÷ 1000 ; since you are dividing by "1000" ; you take the number as it is, and move the number back THREE (3) decimal places:
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→ 305. becomes: 0.305 .
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Alternately, 305/1000 can be written in fraction form:
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Both number are divisible by "5" ;
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305/1000 = (305÷5) / (1000÷5) = 61/200 .
___________________________________________________
__________________________________________________
Note: 305/1000 would be 305 ÷ 1000 ; since you are dividing by "1000" ; you take the number as it is, and move the number back THREE (3) decimal places:
________________________________________________
→ 305. becomes: 0.305 .
________________________________________________
Alternately, 305/1000 can be written in fraction form:
________________________________________________
Both number are divisible by "5" ;
________________________________________________
305/1000 = (305÷5) / (1000÷5) = 61/200 .
___________________________________________________
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For the proof here kindly check the attachment.
We are given that. Also, the transversal is shown. Let us take the first case, that of
and
. Please note that all other proofs will follow in a similar manner.
Let us begin, please have a nice look at the diagram. We will see that and
are vertically opposite angles. We know that vertically opposite angles are congruent. Thus,
and
are congruent angles.
=
Now, we know that and
are alternate interior angles. We also, know that alternate interior angles are equal too. Thus, we have:
=
From the above arguments it is clear that:
=
=
.
Thus, =
We have proven the first instance. Please note that all other instances can be proved in a similar fashion.
For example, for and
we can take
and
as vertically opposite angles thus making
=
. Now,
and
are alternate interior angles and thus
and
are equal. Thus, we have
and
.
