error in emulator

04232016, 02:24 AM
Post: #1




error in emulator
I entered 3*sqrt3*sqrt3 and got an answer of 9.00000000001
does the real Prime make this same funny answer? 

04232016, 03:10 AM
Post: #2




RE: error in emulator
(04232016 02:24 AM)SalivationArmy Wrote: I entered 3*sqrt3*sqrt3 and got an answer of 9.00000000001This funny answer is find in Home by me. In CAS, it make the correct answer: 9. Remember the Home mode give an approximated result, while CAS don't. The definition of Home mode can be an explanation to this funny result. 

04232016, 04:20 AM
Post: #3




RE: error in emulator  
04232016, 05:49 AM
(This post was last modified: 04232016 06:18 AM by SalivationArmy.)
Post: #4




RE: error in emulator
I understand now.
Instead of logically multiplying 3 x 3 and placing the result under the sqrt like a human brain would, it's calculating the result of each of the sqrt3 to 10 or so digits the rounding off, which is NOT a perfect result, then working the problem. human: 3* sqrt3 *sqrt3 = 3 * sqrt9 = 3 * 3 = 9 Honest calculator: 3* sqrt3 *sqrt3 = 3 * 1.73205080757 * 1.73205080757 = 9.00000000001 (The bolded digits are rounded off) Nasa calculated the square root of three out to 10 million digits, you can imagine it a mess of a number. Here's the first 500 digits: 1.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485756 7562614141540670302996994509499895247881165551209437364852809323190230558206797482010108467492326501 5312343266903322886650672254668921837971227047131660367861588019049986537379859389467650347506576050 7566183481296061009476021871903250831458295239598329977898245082887144638329173472241639845878553976 6795806381835366611084317378089437831610208830552490167002352071114428869599095636579708716849807289 

04232016, 06:10 AM
Post: #5




RE: error in emulator
(04232016 02:24 AM)SalivationArmy Wrote: I entered 3*sqrt3*sqrt3 and got an answer of 9.00000000001 This answer is not funny, it's simply correct. Like any other finiteprecision calculator the Prime does not return sqrt 3. It returns a value that matches sqrt 3 in its first twelve digits, i.e. 1,73205080757. But that's not sqrt 3 = 1,7320508075688772935274463415... etc. etc. Now the Prime gives the exact answer based on this approximation of sqrt 3: 3 x 1,73205080757 = 5,19615242271 5,19615242271 x 1,73205080757 = 9,0000000000116675... Which, rounded to 12 digits, is the result you see (9,00000000001). Try sqrt 7 x sqrt 7 or sqrt 8 x sqrt 8. If your calculator works correctly you should not get 7 and 8 but 6,99999999998 and 8,00000000002. Dieter 

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