HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 35
Pitfalls in Fraction mode, if you are converting an exact decimal to a fraction, then set
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The Fraction setting is thus far more powerful than most calculators but can require that you understand what is happening. It should also be clear now why a special fraction button was not provided: the 'fractions' are never actually stored or manipulated as fractions at all! Pitfalls in Fraction mode As you can see above right, a setting of Fraction 4 produces a strange (but actually correct) result for 0.666, while adding one more 6 (to take the decimal beyond 4 d.p.) will give the desired result of 2/3. In other words, so long as you understand the approach taken by the hp 39gs and hp 40gs it is capable of producing results which are closer to what was probably intended by the user in entering 0.66666. You may have noticed that all the results so far have been improper fractions. For example the first calculation shown right gives the answer as 22/15 rather than 1715 . The fraction setting of Mixed Fraction is essentially the same but answers are given as mixed fractions instead of improper fractions, as shown. If you want to use the Fraction setting to convert decimals to fractions, here are some tips... • if converting a recurring decimal to a fraction, then make sure you include at least one more digit in the decimal than the setting of Fraction in MODES. As you can see right, failing to include enough decimal places does not produce the desired result. • if you are converting an exact decimal to a fraction, then set a Fraction n value of at least one more than the number of decimal places in the value entered. Both examples in the third screen shot to the right were done at Fraction 6. Not understanding the significance of the setting of Fraction can produce some unfortunate effects. For example, at Fraction 2, the value of 123.456 becomes 123, with the 0.456 dropped entirely. An example of this is shown right. If you use a setting of only Fraction 2 to perform the calculation shown, you will find to your amazement that 1/3 + 4/5 = 8/7 , whereas using Fraction 6 gives the correct answer. 35