<P> The ratio of a circle's circumference to its diameter is called pi, and is not only irrational but also transcendental . </P> <P> Another well - known example is the golden ratio, which is defined as both sides of the equality a: b = (a + b): a . Writing this in fractional terms as (a / b) = 1 + 1 (a / b) (\ displaystyle (a / b) = 1 + (\ frac (1) ((a / b)))) and finding the positive solution gives the golden ratio a b = 1 + 5 2, (\ displaystyle (\ tfrac (a) (b)) = (\ tfrac (1 + (\ sqrt (5))) (2)),) which is irrational . Thus at least one of a and b has to be irrational for them to be in the golden ratio . An example of an occurrence of the golden ratio is as the limiting value of the ratio of two successive Fibonacci numbers: even though the n - th such ratio is the ratio of two integers and hence is rational, the limit of the sequence of these ratios as n goes to infinity is the irrational golden ratio . </P> <P> Similarly, the silver ratio is defined as both sides of the equality a: b = (2a + b): a . Again writing it in fractional terms and obtaining the positive solution, we obtain a b = 1 + 2, (\ displaystyle (\ tfrac (a) (b)) = 1 + (\ sqrt (2)),) which is irrational, so of two quantities a and b in the silver ratio at least one of them must be irrational . </P> <P> Odds (as in gambling) are expressed as a ratio . For example, odds of "7 to 3 against" (7: 3) mean that there are seven chances that the event will not happen to every three chances that it will happen . The probability of success is 30% . In every ten trials, there are expected to be three wins and seven losses . </P>

When do we say that a proportion is equal