Select all the statements that are true.
3.333… is irrational because 3.333… is a repeating decimal.
√7 is irrational because 7 is not a perfect square.
√20 is irrational because it is a nonterminating, nonrepeating decimal.
0.111… is rational because 0.111… is a nonterminating decimal.
π is irrational because π is a nonterminating, nonrepeating decimal.
Select all the statements that are true. 3.333… is irrational because 3.333… is a repeating decimal. √7 is irrational because 7 is not a perfect square. √20 is irrational because it is a nonterminating, nonrepeating decimal. 0.111… is rational because 0.111… is a nonterminating decimal. π is irrational because π is a nonterminating, nonrepeating decimal
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Let’s evaluate each statement:
1. 3.333… is irrational because 3.333… is a repeating decimal.
– False: 3.333… (or 3.3 repeating) is a rational number because it can be expressed as the fraction 10/3.
2. √7 is irrational because 7 is not a perfect square.
– True: √7 cannot be expressed as a fraction because 7 is not a perfect square, making √7 an irrational number.
3. √20 is irrational because it is a nonterminating, nonrepeating decimal.
– True: √20 simplifies to 2√5, which is irrational; thus, it is a nonterminating and nonrepeating decimal.
4. 0.111… is rational because 0.111… is a nonterminating decimal.
– True: 0.111… can be expressed as the fraction 1/9, making it a rational number despite being nonterminating.
5. π is irrational because π is a nonterminating, nonrepeating decimal.
– True: π is known to be an irrational number, which is confirmed by its nonrepeating and nonterminating nature.
True statements: √7 is irrational; √20 is irrational; 0.111… is rational; π is irrational.
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