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Finding Two Calculator Fractions (Posted on 2023-03-02) Difficulty: 3 of 5
Lionel has a calculator that displays a maximum of ten digits (for example: 3,478,062,139 and 0.073672932)
• Lionel chose 4 distinct prime numbers p,q,r and s all less than 100 and he calculates p/q – r/s. The result is 0.180451127. Determine p,q,r and s.
• Consider the two base ten numbers 0.728101457 and 0.635149023. One of these numbers is the result displayed by Lionel's calculator of an irreducible fraction u/v with u and v, that are positive integers less than 1000. The decimals of the other number are taken from a table of random numbers.

Determine the terms u and v of the irreducible fraction.

  Submitted by K Sengupta    
Rating: 5.0000 (1 votes)
Solution: (Hide)
Part 1: p= 17, q = 19, r= 5, s= 7, so that: 17/19 - 5/7=0.180451127.

Part 2: 618/973 = 0.6351490236....

No truncation of the first continued fraction of 0.728101457 matches all ten digits without the numerator and denominator exceeding 1000, so it must be just some random digits.

For an explanation, refer to the solution submitted by Brian Smith in this location.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionContinued Fractions SolutionBrian Smith2023-03-02 23:49:59
SolutionsolutionsCharlie2023-03-02 15:38:38
SolutionBoth partsLarry2023-03-02 14:34:15
Some ThoughtsFirst PartLarry2023-03-02 14:19:05
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