one third - is only one answer
any value of x such that 1/4 < x < 1/2 or 0.25 < x < 0.5
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one quarter
one quarter is less than one third
i quarter of a cent
no such thing. Think again - An Australian 20c coin. Its value is also less than a US quarter but more than a US dime. I suspect there are many other examples.
3 inches to the nearest inch and 3 inches to the nearest half inch both refer to a length not less than 2.5 inches and less than 3.5 inches. 3 inches to the nearest quarter inch refers to a length not less than 2.75 inches and less than 3.25 inches.