HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 183

Some further functions are available in the Hyperbolic group of functions. They are duplicates of functions available on the face of the calculator but give more accurate answers. They would primarily be of use to those people, such as architects and engineers, for whom high accuracy is paramount. These are: EXP() This function gives a more accurate answer than the key labeled e^ which appears above the LN key on the calculator. As you can see on the right, the difference is normally not detectable even to 12 significant figures. The difference is only apparent for some values and even then is hardly earth-shattering. ALOG() This function provides the same result as the key labeled 10^ on the keyboard above the LOG key. It is another function giving greater accuracy than the one it 'replaces'. This greater accuracy would probably never be required in a school setting. EXPM1() This function is designed to be more accurate when anti-logging very small values close to zero. It gives the value not of ex but of ex −1 (EXPM1 = exp minus 1). You may wonder how this is an advantage, since you must then add 1 to obtain the correct answer, but a look at the screen opposite will show you. As you can see, the normal keyboard function e^ gives an answer to e0.0000003 of 1.0000003. This gives the impression that it is an exact value (since it doesn't show a full 12 significant digits). The true answer is 1·000000300000045.... but the final digits have been lost in the rounding off to 12 sig. figures. By giving an answer of ex −1, the leading 1 is lost, freeing the calculator to show more accuracy by dropping the leading zeros. This is not normally be needed in the classroom. 183