_ _ _ . _
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>>...The digit in the tens place is twice as big as the digit in the 
tenths place...<<


>>...The digit in the ones place is 1/2 the digit in the tenths place...<<

So the digit in the tenths place is a digit that can be halved to give a
digit and doubled to give a digit.

The fact that it must be able to be halved tells us it's even.
The fact that it must be small enough so that when doubled, the result 
will be a digit, tells us it's 4 or less.

So the tenths digit must be 2 or 4

If the tenth digit were 2, then the digit in the ones place would be
half of 2, or 1 
 
But that can't be because 

>>...The digit in the hundredths place is 1/2 the digit in the ones place...<<

and half of 1 is not a digit.

Therefore the tenths digit has to be 4, 

_ _ _ . 4
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and the tens digit is twice that, or 8, 

_ 8 _ . 4
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and the ones digit is half the 4 in the tenths place or 2, 

_ 8 2 . 4
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and the hundreds digit is 1/2 the 2 in the ones place, or 1.
So we have it

1 8 2 . 4
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Answer 182.4

So we didn't even need this:

>>...The digit in the hundreds place is the largest odd digit...<<

It's not just the LARGEST odd digit, it's the ONLY odd digit.  And
what else is ODD is that 1 is the SMALLEST odd digit of all odd numbers,
and here it gets to be the LARGEST, so how can the SMALLEST of all be
LARGER than any, let alone LARGEST of any other odd number?  It can't. 
So it's LARGER than NONE???  Is that really a case of 'LARGER', let alone
a case of 'LARGEST'
Just being silly! 
J    
Edwin