Question

rational and irrational numbers notes
rational numbers:
can be expressed as the quotient of two integers (i.e. a fraction) with a denominator that is
not zero.
many people are surprised to know that a repeating decimal is a rational number
examples: -5, 0.7, 3/2, 0.26

• √9 is rational - you can simplify the square root to 3 which is the quotient of the integers 3

and 1.
irrational numbers:
cant be expressed as the quotient of two integers (i.e. a fraction) such that the
denominator is not zero.
examples: √7, √5, π, 0.34989238, 0.120102001211, 3.14151692345
sort the numbers into rational or irrational. write the numbers in the appropriate bubble.
0.8, √64, 0, √32, -19, -√100, 2.343443444...
3/7, √75, 6 2/7, 12.67, √121, 12/5, π
directions: for each number shown, classify it as either rational or irrational, then tell whether or not it is
terminating or repeating.

1. -0.6 rational or irrational (circle one) terminating, repeating, or neither
2. √100 rational or irrational (circle one) terminating, repeating, or neither
3. 2/5 rational or irrational (circle one) terminating, repeating, or neither
4. -2/3 rational or irrational (circle one) terminating, repeating, or neither
5. 0.35217534... rational or irrational (circle one) terminating, repeating, or neither

Explanation:

Step1: Analizar el primer número

-0.6 se puede escribir como \(-\frac{6}{10}=-\frac{3}{5}\), que es una fracción de enteros. Además, es un decimal terminado.

Step2: Analizar el segundo número

\(\sqrt{100} = 10\), que es un entero. Los enteros son racionales y 10 es un decimal terminado.

Step3: Analizar el tercer número

\(\frac{2}{5}=0.4\), que es una fracción de enteros. Es un decimal terminado.

Step4: Analizar el cuarto número

\(-\frac{2}{3}=-0.\overline{6}\), que es una fracción de enteros. Es un decimal periódico.

Step5: Analizar el quinto número

0.35217534… no se puede expresar como una fracción de enteros y no es un decimal terminado ni periódico.

Answer:

1. rational, terminating
2. rational, terminating
3. rational, terminating
4. rational, repeating
5. irrational, neither