HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 34
HP 40gs - Graphing Calculator Class Manual
UPC - 882780045217
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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 '4' in Fraction 4. Very 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 MODES view of... Fraction 1 changes 0.234 to 3 13 which is actually 0.2307692... (matching to at least 1 significant figures.) Fraction 2 changes 0.234 to 7 30 which is actually 0.2333333... (matching to at least 2 significant figures.) Fraction 3 changes 0.234 to 11 47 which is actually 0.2340425... (matching to at least 3 significant figures.) Fraction 4 changes 0.234 to 117 500 ⎛ ⎝⎜ or 234 ⎞ 1000 ⎠⎟ which is exactly 0.234 (thus finally matching to the required 4 significant figures.) Essentially, the value of 4 in Fraction 4 affects the degree of precision used in converting the decimal to a 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. 34