Casio fx85GTPLUS 40 plus digit accuracy

[thenozone]

Casio fx85GTPLUS 40 plus digit accuracy
was using my Casio fx GT Plus in the shed the other day an was shocked to see what my calculation had yielded, an over 40 digit answer when I pressed the StoD Button, see pictures attached.
And I don't think it is the fumes in the shed

[EdS2]

Ah - see that dot over the final digit? That shows you're in 'recurring decimal mode' - and indeed, 220/381 repeats over 42 digits.

Neat though!

Edit: you might be able to get to 47 digits, maybe 48, but probably not 50, with an appropriate calculation. See the manual.

[ijabbott]

(05-14-2023 07:35 AM)EdS2 Wrote:  Ah - see that dot over the final digit? That shows you're in 'recurring decimal mode' - and indeed, 220/381 repeats over 42 digits.

Neat though!

Edit: you might be able to get to 47 digits, maybe 48, but probably not 50, with an appropriate calculation. See the manual.

I'm sure there is a nice challenge here to display the maximum possible number of digits!

fx-83GT PLUS fx-85GT PLUS User's Guide Wrote:Conditions for Displaying a Calculation Result as a Recurring Decimal
If a calculation result satisfies the following conditions, pressing S↔D will display it as a recurring decimal value.

• The total number of digits used in the mixed fraction (including integer, numerator, denominator, and separator symbol) must be no more than 10.
• The data size of value to be displayed as the recurring decimal must be no larger than 99 bytes. Each value and the decimal point require one byte, and each digit of the period requires one byte. The following, for example, would require of total of 8 bytes (4 bytes for the values, 1 byte for the decimal point, 3 bytes for the period): \(0.\dot{1}2\dot{3}\)
  

[EdS2]

Yes, a nice idea for a mini-challenge! Perhaps something like

Quote:Find a fraction with a specific length of repeating decimal digits. You have a maximum total of 9 digits for both numerator and denominator. The aim is to get a 99 byte representation, or the largest that doesn't exceed 99, where each digit of the answer, and the decimal point, and each digit of the recurring part, each cost one byte.

For example, 1/44 uses only 3 digits - less than 9, so that's OK.
The decimal expansion is 0.0227... which is 0.02 then recurring 27. So that's 5 bytes for the number, one for the decimal point, and two more for the recurring part. Total score 8 bytes, which is very far short of the 99 bytes target.

But 1/47 is 0.many where many is 46 recurring digits, so that costs 47 + 1 + 46, a score of 94 bytes. Much better!

Edit: found an answer by trial and error: gelbaruhaqerqnaqavargrraguf (rot13)