True or false
1.)
The set of integers contains the set of rational numbers
2.)Every repeating decimal is a rational number
3.)Every square root is an irrational number
4.) the set of whole numbers contains the set of rational number
5.)every terminating decminal is arational number
1)true
2)true
3)true
4)true
5)true
1.) True. The set of integers does indeed contain the set of rational numbers. In fact, every integer can be expressed as a fraction where the denominator is 1.
2.) True, but also kinda false. Every repeating decimal can be written as a rational number, but not every rational number is a repeating decimal. Some of them are sneaky little non-repeating ones, trying to hide their true nature.
3.) False. While some square roots like √2 or √3 are indeed irrational numbers, there are also square roots like √4 or √9 that are rational. They can be quite rational about it.
4.) True. The set of whole numbers is like the cool older sibling of rational numbers, embracing them with open arms. It includes all positive integers, zero, and their negative counterparts. Rational numbers are just a subset of the whole shebang.
5.) True. Every terminating decimal can be written as a rational number. But don't be fooled, not all rational numbers are as terminal as those decimals. Some like to stick around and cause trouble, being all non-terminating and repeating. Stand your ground, my friend!
1.) True. To determine if the set of integers contains the set of rational numbers, we need to understand the definition of each set. Integers are numbers without fractional or decimal parts, including positive and negative whole numbers and zero. Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. Every integer can be written as a fraction by placing it over 1. Therefore, every integer can be expressed as a rational number, making the statement true.
2.) True. To determine if every repeating decimal is a rational number, we need to understand the properties of rational numbers and repeating decimals. Rational numbers can be expressed as a fraction of two integers. A repeating decimal has a recurring pattern of digits after the decimal point. Any repeating decimal can be written as a fraction by using the repeating part of the decimal as the numerator and a denominator with as many nines as there are repeating digits. Hence, every repeating decimal can be expressed as a fraction, making the statement true.
3.) False. To determine if every square root is an irrational number, we need to understand the properties of irrational numbers and square roots. Irrational numbers cannot be expressed as a fraction or ratio of two integers. A square root is the value that, when multiplied by itself, gives the original number. While some square roots are rational (e.g., √4 = 2), others are irrational (e.g., √2). Therefore, not every square root is an irrational number, making the statement false.
4.) True. To determine if the set of whole numbers contains the set of rational numbers, we need to understand the definition of each set. Whole numbers are non-negative numbers without fractional or decimal parts, including zero and positive integers. Rational numbers are numbers that can be expressed as a fraction of two integers. Since every whole number can be expressed as a fraction by placing it over 1, with a denominator of 1, every whole number can be expressed as a rational number. Hence, the statement is true.
5.) True. To determine if every terminating decimal is a rational number, we need to understand the properties of rational numbers and terminating decimals. Rational numbers can be expressed as a fraction of two integers. Terminating decimals have a finite number of digits after the decimal point. Any terminating decimal can be written as a fraction by placing its digits after the decimal point over a denominator of 10 raised to the power of the number of decimal places. Therefore, every terminating decimal can be expressed as a fraction, making the statement true.