Math Problem : G.10 Fraction denoted by the decimal

When a certain fraction was denoted by the decimal and the 3rd decimal place was rounded off, it was to be 0.32.
Find the smallest denominator among such fractions.

Answer

6/19

Solution

The fraction to be found is that it is 0.315 or more and smaller than 0.325 when it is changed to a decimal.
In order to find the fraction of which denominator is smallest, the numerator should also be the smallest number as less as possible.
When the numerator is 1, the fraction close to 0.315 is 1/3.
Since 1/3 = 0.3333---, it does not suit conditions.
When a numerator is 2, the fraction close to 0.315 is 2/6 and as checked above, it does not suit conditions.
When a numerator is 3, the fraction close to 0.315 is 3/10, it is 3/10 = 0.3 and does not suit conditions.
when a numerator is 4, the denominator which is likely to be applied to conditions is 

13.4 / 13 = 0.30----.
It does not suit conditions.
When a numerator is 5, the denominator which is likely to be applied to conditions is 

16.5 / 16 = 0.312---.
It does not suit conditions.
When a numerator is 6, the denominator which is likely to be applied to conditions is           19.6 / 19 = 0.315----.
This will be set to 0.32 if the 3rd decimal place is rounded off.
Therefore the fraction to be found is 6/19.