percent.inYou will frequently see claims using percentages like: "56.3% of all Florida tourists prefer Daytona Beach!" But what do these claims really mean? In this program, you should determine the minimum sample size necessary to give a given percentage with a given number of decimal digits.
For this problem, percentages are computed by taking an integer divided by the sample size. For example, a percentage of 50% with 0 decimal digits could be obtained from a sample size of just 2, since 1/2 = 50%, but a percentage of 51% with 0 decimal digits would need a sample size of 35, since to get a value that would round to 51%, you need to use 18/35. No smaller sample size would give a percentage of 51%. Similarly, to get a percentage of 50.0% with 1 decimal digit, a sample size of 2 would still suffice, but it would take a sample size of 49 to get a percentage of 51.0% with one decimal digit. You should follow standard rounding rules where values of 5 and above round up to the next higher value and all others round down.
The input to your program will be a list of 1 or more data sets where each data set consists of two numbers d and p. d is an integer, 0 <= d <= 5, indicating the number of significant decimal digits in the percentage, which is represented by p, 0 < p < 100, a floating point number.
The end of input will be indicated by the data set 0 0.
For each line of input (except for the end of input indicator line), your program should produce a line of output in the following form:
A minimum sample size of n is necessary for a percentage of p.
where n is replaced with the minimum sample size and p is the input value p, with d decimal digits.
0 51 2 51.00 1 56.3 0 0
A minimum sample size of 35 is necessary for a percentage of 51. A minimum sample size of 100 is necessary for a percentage of 51.00. A minimum sample size of 16 is necessary for a percentage of 56.3.