# Rational Or Irrational?

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This quiz will evaluate students' ability to identify rational numbers and differentiate them from irrational numbers.

• 1.

### Which of the following numbers is not a rational number?

• A.

1/2

• B.

.25

• C.

√ 2

• D.

-23

C. √ 2
Explanation
A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, rational numbers are numbers that can be written in the form a/b, where "a" and "b" are integers and "b" is not equal to zero. √2 (the square root of 2) cannot be expressed as the quotient of two integers, and it is an example of an irrational number. Irrational numbers cannot be exactly represented as fractions of integers and have non-repeating, non-terminating decimal expansions.

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• 2.

### Select the rational number.

• A.

782

• B.

3.14159265...........

• C.

9.965468

• D.

1.28374927495837........

A. 782
Explanation
The number 782 is a rational number because it can be expressed as a fraction, where the numerator and denominator are both integers. In this case, 782 can be written as 782/1, which satisfies the definition of a rational number.

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• 3.

### Which number is irrational?

• A.

-3

• B.

4

• C.

-22

• D.

9.946787839395329

D. 9.946787839395329
Explanation
The number 9.946787839395329. An irrational number is a real number that cannot be expressed as a fraction of two integers, and its decimal representation is non-terminating and non-repeating. These numbers possess infinite and non-patterned decimal expansions, challenging traditional notions of numerical representation.

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• 4.

### Pi is a rational number.

• A.

True

• B.

False

B. False
Explanation
Pi is not a rational number. A rational number is defined as a number that can be expressed as a fraction where both the numerator and denominator are integers. However, Pi is an irrational number, meaning it cannot be expressed as a fraction and its decimal representation goes on indefinitely without repeating. Therefore, the correct answer is False.

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• 5.

### All of the following numbers are rational. 1/6 .425 -1 1,234,234,509

• A.

True

• B.

False

A. True
Explanation
All of the numbers given in the options are rational numbers. A rational number is any number that can be expressed as a fraction or a ratio of two integers. The first option, 1/6, is a fraction and can be written as the ratio of the integers 1 and 6. The second option, 0.425, can be written as the fraction 425/1000, which can be simplified to 17/40. The third option, -1, can be written as -1/1. The fourth option, 1,234,234,509, is an integer and can be written as the fraction 1,234,234,509/1. Therefore, all of the given numbers are rational numbers, making the statement "All of the following numbers are rational" true.

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• 6.

### All of the following numbers are rational. 4, -16

• A.

False

• B.

True

B. True
Explanation
The given numbers are 4 and -16. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. Both 4 and -16 can be expressed as fractions, so they are rational numbers.

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• 7.

### Repeating decimals such as 0.2222222 are rational.

• A.

True

• B.

False

A. True
Explanation
Repeating decimals can be expressed as a fraction, making them rational numbers. In this case, the repeating decimal 0.2222222 can be written as the fraction 2/9, which shows that it is indeed rational.

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• 8.

### Numbers that may be expressed as fractions are rational.

• A.

True

• B.

False

A. True
Explanation
Numbers that may be expressed as fractions are rational because a rational number is defined as any number that can be expressed as a fraction, where the numerator and denominator are both integers. Fractions are written in the form of a/b, where a and b are integers and b is not equal to zero. Therefore, any number that can be written in this form is considered rational.

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• 9.

### Negative numbers may not be classified as rational numbers.

• A.

True

• B.

False

B. False
Explanation
Negative numbers can be classified as rational numbers. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. Negative numbers can be written as a fraction with a negative numerator and a positive denominator, making them rational. Therefore, the statement that negative numbers may not be classified as rational numbers is false.

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• 10.

### All positive numbers are rational.

• A.

True

• B.

False

B. False
Explanation
The statement "All positive numbers are rational" is false. A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers. However, there are positive numbers that cannot be expressed in this form, such as the square root of 2 or pi. These numbers are called irrational numbers. Therefore, not all positive numbers are rational, making the statement false.

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• 11.

### Now that you know what rational numbers are, provide two ways that you have used rational numbers outside of school. (You provide one and your partner provide the other. Type your name beside your answer.)

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• Feb 22, 2024
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• Apr 17, 2012
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