HP 39gs Master Manual page 34

The second point to remember involves the method the hp 39gs and hp 40gs use when converting decimals to
fractions, which is basically to generate (internally and unseen by you) a series of continued fractions which
are approximations to the decimal entered. The final fractional approximation chosen for display is the first
one found which is 'sufficiently close' to the decimal. Look up 'continued fractions' on the web or in a
textbook if you don't know what these are.
The trap lies in what constitutes 'sufficiently close', and this is determined by the '
roughly explained, the calculator will use the first fraction it finds in its process of approximation which
matches the decimal to that number of significant digits.
For example, a setting in the
Fraction 1
which is actually 0.2307692...
(matching to at least 1 significant figures.)
Fraction 2
which is actually 0.2333333...
(matching to at least 2 significant figures.)
Fraction 3
which is actually 0.2340425...
(matching to at least 3 significant figures.)
Fraction 4
which is exactly 0.234
(thus finally matching to the required 4 significant figures.)
Essentially, the value of
fraction. As was said earlier, the calculator will use the first fraction it finds in its process of approximation
which matches the decimal to that number of significant digits.
view of...
MODES
changes 0.234 to
changes 0.234 to
changes 0.234 to
changes 0.234 to
in affects the degree of precision used in converting the decimal to a
4 Fraction 4
3
13
7
30
11
47
117 ⎛ 234 ⎞
⎜ or ⎟
500 ⎝ 1000 ⎠
34
' in . Very
4 Fraction 4