Question

1. a teacher places seven cards, lettered a–g, on a table. which cards show irrational numbers?

Explanation:

Step1: Recall irrational number definition

Irrational numbers are non - repeating, non - terminating decimals and cannot be expressed as a fraction \(\frac{p}{q}\) (\(p,q\) integers, \(q
eq0\)). Rational numbers include integers, fractions, terminating decimals, and repeating decimals.

Step2: Analyze each card

• Card A: \(10\) is an integer, so it is rational.
• Card B: \(\frac{6}{5}=1.2\), a terminating decimal (rational).
• Card C: \(\pi = 3.1415926\cdots\) is a non - repeating, non - terminating decimal, so it is irrational.
• Card D: \(\frac{11}{4}=2.75\), a terminating decimal (rational).
• Card E: \(8.25635\cdots\) is a non - repeating, non - terminating decimal, so it is irrational.
• Card F: \(- 7\) is an integer, so it is rational.
• Card G: \(6.\overline{31}\) is a repeating decimal (rational).

Answer:

C. \(\boldsymbol{\pi}\), E. \(\boldsymbol{8.25635\cdots}\)