determine whether each statement is sometimes, always, or never true:
1) a whole number is an integer.
2) a repeating decimal is a real number.
plz help me..... tnx
http://www.mathgoodies.com/lessons/vol5/intro_integers.html
http://www.mathsisfun.com/numbers/real-numbers.html
A whole number is an integer.......A repeating decimal is a real number. Real numbers are either rational or irrational
To determine whether each statement is sometimes, always, or never true, we need to understand the definitions of the terms involved and their relationships. Let's break it down:
1) A whole number is an integer.
Explanation:
- A whole number is a number that is not a fraction or a decimal. It includes all positive numbers (including zero) and their negatives.
- An integer is a number that includes all whole numbers and their negatives, as well as zero.
Based on these definitions, we can conclude that a whole number is indeed an integer. This statement is always true.
2) A repeating decimal is a real number.
Explanation:
- A decimal is a number expressed in the base-10 numeral system using the digits 0-9 and a decimal point.
- A repeating decimal is a decimal number in which one or more digits repeat infinitely.
- A real number is a number that includes all rational and irrational numbers, which can be represented by decimals.
From the definitions, we can see that a repeating decimal is a subset of real numbers since not all real numbers have repeating decimal representations (e.g., irrational numbers like √2). Therefore, this statement is sometimes true.
In summary:
1) A whole number is always an integer.
2) A repeating decimal is sometimes a real number.
Remember, understanding the definitions of terms and their relationships is crucial in determining the correctness of statements.