A fraction can be written as a decimal that ends or repeats. Some numbers do not do either. In this course we learn to tell the two kinds apart, and we find irrational numbers such as the square root of 2 on the number line.
3 lessons, about 1 h 15 min3 simulations10 problems6 practice questionsPython in every lesson
Created by StemPy LabA rational number can be written as p over q with q not zero. Its decimal either ends or repeats. A fraction ends exactly when its denominator, in lowest terms, has only the factors 2 and 5.
A number that cannot be written as p over q is an irrational number. The decimal of a rational number ends or repeats, and the decimal of an irrational number neither ends nor repeats, as for root 2 and pi. The square root of a whole number that is not a perfect square is irrational, while the roots of 4, 9 and 0.25 are rational. The fraction 22 over 7 is only close to pi. Root 2 is irrational by a proof by contradiction: if p over q is in lowest terms then both p and q would be even. Rational and irrational numbers together make the real numbers, and there are irrational numbers between any two numbers.
The rational and irrational numbers together are the real numbers, and every real number is a point on the number line. We can place on the line with a right triangle, and the square roots of other whole numbers with a spiral.
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