Rational and Irrational Numbers
Aligned to 8.NS.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
A rational number can be written as a fraction, but some numbers, like the square root of 2 or pi, cannot, so they are called irrational. Their decimals go on forever without repeating. You can still estimate an irrational number to place it on a number line.
Worked examples
Example 1
Estimate the square root of 2. Since 1 squared is 1 and 2 squared is 4, the square root of 2 is between 1 and 2, around 1.4.
Example 2
0.375 is rational: it equals 3/8, a ratio of two whole numbers.
Example 3
A decimal that repeats forever is still rational — 0.333... is 1/3. It is the decimals that never repeat and never end, like π and √2, that are irrational.
Practice questions
- Is 0.75 rational or irrational?
- Between which two whole numbers is the square root of 10?
- Name one irrational number.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Números Racionales e Irracionales
Un número racional puede escribirse como fracción, pero algunos números, como la raíz cuadrada de 2 o pi, no pueden, por lo que se llaman irracionales. Sus decimales son infinitos y no tienen un patrón que se repita. Aun así, puedes estimar un número irracional para ubicarlo en una recta numérica.
Ejemplo 1: Estima la raíz cuadrada de 2. Como 1 al cuadrado es 1 y 2 al cuadrado es 4, la raíz cuadrada de 2 está entre 1 y 2, aproximadamente 1.4.
Ejemplo 2: 0.375 es racional: equivale a 3/8, una razón de dos números enteros.
Ejemplo 3: Un decimal que se repite para siempre sigue siendo racional — 0.333... es 1/3. Los irracionales son los decimales que nunca se repiten y nunca terminan, como π y √2.
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