2)Name the sets of numbers to which 457 belongs.
(answer)natural,whole,integers,rational,reals
My book says that every REAL number has to be rational or irrational.
Blueridge said that my answer was correct except to exclude rational from my list. From what my book says I HAVE to include rational or irrational right? so which one is it?
457 is indeed a rational number
I thought so. Thank you
Well, it seems like you're caught in a bit of a mathematical clown confusion! Let me try to clarify things for you.
First off, you are absolutely correct that every real number is either rational or irrational. So both rational and irrational numbers are part of the set of real numbers.
However, when listing the sets of numbers to which 457 belongs, you don't need to include both rational and irrational separately. The set of real numbers already encompasses both rational and irrational numbers.
So, the correct answer would be that 457 belongs to the sets of natural, whole, integers, and real numbers. Phew, that's a whole circus of numbers to keep track of, isn't it?
You are correct that every real number can be classified as either rational or irrational. This means that 457 can be classified as a rational number or an irrational number.
Rational numbers are numbers that can be expressed as a ratio of two integers, in this case, as a fraction. Since 457 can be written as 457/1, it is a rational number.
So, the correct answer would be:
- 457 belongs to the set of natural numbers, whole numbers, integers, rational numbers, and real numbers.
The set of numbers to which 457 belongs includes the natural numbers, whole numbers, integers, rational numbers, and real numbers.
To understand why 457 belongs to each of these sets, let's go through each set one by one:
1. Natural numbers: These are the counting numbers starting from 1 (1, 2, 3, 4, ...). Since 457 is a positive whole number, it is a natural number.
2. Whole numbers: Similar to natural numbers, whole numbers include zero as well (0, 1, 2, 3, ...). Since 457 is a positive whole number, it also belongs to this set.
3. Integers: Integers are all the positive and negative whole numbers (..., -3, -2, -1, 0, 1, 2, 3, ...). Since 457 is a positive whole number, it is also an integer.
4. Rational numbers: Rational numbers are numbers that can be expressed as a fraction, where both the numerator and denominator are integers. Since 457 can be written as 457/1, it is a rational number.
5. Real numbers: Real numbers include both rational and irrational numbers. Rational numbers can be expressed as fractions, while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal representations. Since 457 can be expressed as a fraction and has a terminating decimal representation (i.e., 457.0), it is a rational number and, therefore, a real number.
So, to answer your question, the book is correct. From what the book tells you, every real number must be either rational or irrational, but in this case, 457 is a rational number and, hence, a real number.