Real Number System Test Quiz!

Explanation
A whole number is a number that does not have any fractional or decimal parts. It includes all positive numbers, zero, and negative numbers without any decimal or fractional parts. Since 18 is an integer with no decimal or fractional parts, it is considered a whole number. Therefore, the correct answer is True.

Explanation
The statement "−3/2 is an integer" is false. An integer is a whole number that can be positive, negative, or zero, but it cannot be a fraction or a decimal. −3/2 is a fraction, specifically a negative fraction, which means it cannot be considered an integer. Therefore, the correct answer is false.

Explanation
A rational number is any number that can be expressed as the quotient or fraction p/q​ of two integers, a numerator p and a non-zero denominator q. Rational numbers include integers, fractions, and finite or infinitely repeating decimals.
The number 2.434434443…, as described, does not have a pattern that repeats in a regular, predictable manner. If the sequence of digits after the decimal point does not repeat periodically or ends (making it non-repeating and non-terminating), the number cannot be represented as a fraction of two integers. Therefore, based on the description, it appears to be an irrational number, not fitting the criteria of a rational number. However, if there was a typo and the sequence intended was a repeating pattern (like 2.43434343…), then it would be considered rational. But as written, assuming it doesn't form a repeating pattern, it's classified as irrational.

Explanation
An integer is a whole number that can be either positive, negative, or zero. 6.57 is not a whole number as it contains a decimal part, therefore it is not an integer. Hence, the correct answer is False.

Explanation
A rational number is defined as any number that can be expressed as a fraction, where both the numerator and denominator are integers. In the case of 7777, it can be expressed as 7777/1, which is a fraction with both the numerator and denominator being integers. Therefore, 7777 is a rational number.

Explanation
A rational number is defined as any number that can be expressed as a fraction, where the numerator and denominator are both integers. Since all fractions can be expressed in this form, it follows that all fractions are rational numbers. Therefore, the statement "All fractions are rational numbers" is true.

Explanation
The statement is incorrect. While all whole numbers are integers, not all integers are whole numbers. Integers include both positive and negative whole numbers, as well as zero, whereas whole numbers consist only of positive whole numbers and zero.

Explanation
All irrational numbers are real numbers because irrational numbers cannot be expressed as a fraction or a ratio of two integers. They are numbers that cannot be written as terminating or repeating decimals. Real numbers include both rational and irrational numbers, so it is true that all irrational numbers are also real numbers.

Explanation
All negative whole numbers are integers because integers include both positive and negative whole numbers, as well as zero. Negative numbers are a subset of integers, specifically the ones that are less than zero. Therefore, it is true to say that all negative numbers are integers.

Explanation
The set -6, -225, 4, 7, 8 contains all rational numbers as integers are inherently rational. Rational numbers can be expressed as fractions, and integers can be represented as fractions with a denominator of 1. Therefore, this set encompasses a range of rational values.

Explanation
Rational numbers are numbers that can be expressed as the ratio of two integers where the denominator is not zero. Let's analyze each set of numbers:

1. π is not a rational number; it's an irrational number.
2. -3.0541... is an irrational number because it can go on without a fixed pattern, and on decimals with a finite number of digits are rational. 99 is also a rational number, and 0.14363 is rational because it's a finite decimal.
3. -6, -225, 4, 7, and 8 are all rational numbers because they can be expressed as integers.
4. 21 is a rational number because it's an integer. 0.75 and 0 are also rational numbers because they can be expressed as fractions with integers in the numerator and non-zero integers in the denominator.

Explanation
The irrational number in the given set is π. Irrational numbers are numbers that cannot be expressed as a fraction or a decimal that terminates or repeats. π is an irrational number because it is a non-repeating, non-terminating decimal.

Explanation
The statement is true because a rational number is defined as any number that can be expressed as a fraction, where the numerator and denominator are both integers. In this case, -5 can be expressed as -5/1, which is a fraction with integers as both the numerator and denominator. Therefore, -5 is a rational number.

Explanation
In mathematics, an integer is a whole number that can be positive, negative, or zero. Since 0 does not have a fractional or decimal part, it is considered a whole number and therefore an integer. Hence, the statement "0 is an integer" is true.

Explanation
The square root of 16 is a natural number because the square root of any perfect square is always a whole number. In this case, 16 is a perfect square because it can be expressed as the product of 4 and 4. Therefore, the square root of 16 is 4, which is a natural number.

Explanation
An integer is a whole number that can be positive, negative, or zero. Although -3.25 is a negative number, it is not a whole number. Therefore, the correct answer is False.

Explanation
The square root of 8 is not a rational number. A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers. However, the square root of 8 is an irrational number because it cannot be expressed as a fraction. It is a non-repeating, non-terminating decimal.

Explanation
The square root of 7 is a real number because it can be expressed as a non-repeating, non-terminating decimal. In decimal form, the square root of 7 is approximately 2.645751311. Real numbers include all rational and irrational numbers, and since the square root of 7 is an irrational number, it falls under the category of real numbers.

Explanation
The best classification for -4 is integer because it is a whole number that can be positive, negative, or zero. It is also a rational number because it can be expressed as a fraction, in this case -4/1. Lastly, -4 is a real number because it can be plotted on the number line and is not an imaginary number.