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Project: Fractions
Unit: DelphiDabbler.Lib.Fractions
Record: TFraction
Applies to: ~>0.1
function RoundToMultiple(const F: TFraction): TFraction;
This method rounds the fraction to the nearest whole number multiple of the given fraction F and returns the result.
For example, if you round 11/16 to a whole number multiple of 1/8 the result is 6/8.
RoundToMultiple can be useful if you have performed a calculation using fractions but want the result accurate to a certain degree, for example the nearest eighths or sixteenths. It is also useful for converting floating point numbers to fractions with the required accuracy, for example to express π as a fraction to the nearest seventh.
Express π in terms of fractions to the nearest 1/N where N = 1 to 10.
var
FPi, FRound: TFraction;
N: Integer;
begin
FPi := PI; // Pi is automatically converted to fraction
for N := 1 to 10 do
begin
FRound := FPi.RoundToMultiple(TFraction.Create(1, N));
WriteLn(
Format(
'Pi in terms of 1/%d = %d/%d',
[N, FRound.Numerator, FRound.Denominator]
)
);
end;
end;