33.3333333333 … with the 3s repeating is still a rational number. That means that some sets of infinity are bigger than other sets of infinity! How is that for a mind boggling thought!Ĭan you put irrational numbers in fraction form? No! You cannot express rational numbers as a fraction because fractions are ratios between two numbers. Rational numbers are theoretically countable and irrational numbers are not, so some mathematicians say there are more irrational numbers than rational numbers. Numbers are infinite so there are infinite amounts of both rational and irrational numbers. How many irrational numbers are there? One might think that there would be more rational numbers than irrational numbers, but the opposite is true. How far did they calculate out before making that decision … 1000 places ….10, 000 places? How did early mathematicians discover that irrational numbers exist?Īt what point did they give up and decide that the numbers to the right of the decimals would never repeat and never stop? Here are a few questions about irrational numbers to spark your interest. They provide people who are hesitant about math some interesting things to think about. They provide math lovers, like us, some fascinating creative exercises, like proving that a number is irrational. Just thinking that irrational numbers exist sparks some interesting questions.
They either leave the number in the symbolic form or decide how accurate (how many digits) they need to use. Scientists, accountants, and engineers rely on e for much of their work. Who doesn’t love making money? For those not satisfied with just going out three places past the decimal point, here is a link to the first five million digits.Īre there Practical Uses for Irrational Numbers? We like e because it is used for calculating continuous compounding interest such as for calculating the return on an investment. We like this number because you can prove it is irrational.Ĥ) The number e or Euler’s number, is the base of natural logarithms. The approximate square root of 2 is 1.414. 1/Φ=Φ-1ģ) The square root of 2 is another well-known irrational number.
Φ 2 = Φ + 1 and the reciprocal (1 divided by the number) of Phi is one less than itself. We like Phi because it has two properties that no other positive number has. For basic calculations the number 1.618 is used for Phi. In fact there are mathematical correlations between Fibonacci sequence and Φ. It is known as the “the Golden Number” because the geometric relationships are seen in art, nature, architecture, physics, theology, and more! Some people may relate “the Golden Number” to the Fibonacci sequence.
For basic calculations the number 3.142 is used for pi.Ģ) Phi Φ (pronounced fie) describes the ratio of line segments divided in a specific way. That just boggles the mind.ġ) Pi describes the ratio of a circle’s circumference in relationship to its diameter. We like the idea that irrational numbers go on forever. That means whole numbers are never irrational numbers because the only number after the decimal would be 0. It is number where the digits to the right of the decimal go on indefinitely without a repeating pattern. We celebrate “pi day” on March 14th each year with pie and activities related to this irrational number, but we like other irrational numbers too!Īn irrational number is a number that can’t be expressed as a ratio between two numbers. At Mathnasium of Littleton some of our favorite numbers are irrational.
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