For each number, circle the subset(s) of the real numbers that the number belong to.
26) √49 rational, integers, whole numbers, natural numbers, irrational
27) −√81 rational, integers, whole numbers, natural numbers, irrational
28) √43 rational, integers, whole numbers, natural numbers, irrational
29) −2/3 rational, integers, whole numbers, natural numbers, irrational
30) 0.27 rational, integers, whole numbers, natural numbers, irrational
31) 5/13 rational, integers, whole numbers, natural numbers, irrational
26) √49: rational, integers, whole numbers, natural numbers
27) −√81: rational, integers, whole numbers, natural numbers
28) √43: irrational
29) −2/3: rational, integers, whole numbers, natural numbers
30) 0.27: rational
31) 5/13: rational, integers, whole numbers, natural numbers
26) √49: rational, integers, whole numbers, natural numbers
27) −√81: rational, integers, whole numbers, natural numbers
28) √43: irrational
29) −2/3: rational, integers, whole numbers, natural numbers
30) 0.27: rational, irrational
31) 5/13: rational, integers, whole numbers, natural numbers
To determine the subsets of real numbers that each given number belongs to, we need to understand the definitions of these subsets.
1. Rational numbers: These are numbers that can be expressed as fractions or ratios of two integers, where the denominator is not zero. Rational numbers include integers, whole numbers, and natural numbers.
2. Integers: These are numbers that can be positive, negative, or zero, without any fractional or decimal parts. Integers include whole numbers and natural numbers.
3. Whole numbers: These are numbers that are positive integers (including zero). Whole numbers include natural numbers.
4. Natural numbers: These are positive integers greater than zero. Natural numbers do not include zero.
5. Irrational numbers: These are numbers that cannot be expressed as fractions or ratios of two integers. Irrational numbers include square roots of prime numbers, non-repeating and non-terminating decimals, and other such numbers.
Now let's go through each number and identify the subsets it belongs to:
26) √49
- The square root of 49 is 7, which is a rational number and an integer.
- Therefore, 26) √49 belongs to the subsets: rational, integer.
27) -√81
- The square root of 81 is 9, which is a rational number and an integer.
- The negative sign indicates that the number is negative, so it also belongs to the negative integers.
- Therefore, 27) -√81 belongs to the subsets: rational, integer, negative integers.
28) √43
- The square root of 43 is an irrational number since it cannot be expressed as a fraction or ratio.
- Therefore, 28) √43 belongs to the subset: irrational.
29) -2/3
- -2/3 is a fraction, so it is a rational number.
- Therefore, 29) -2/3 belongs to the subset: rational.
30) 0.27
- 0.27 is a decimal representation of a rational number because it can be expressed as 27/100 (fraction).
- Therefore, 30) 0.27 belongs to the subset: rational.
31) 5/13
- 5/13 is a fraction, so it is a rational number.
- Therefore, 31) 5/13 belongs to the subset: rational.
To summarize:
26) √49: rational, integer
27) -√81: rational, integer, negative integers
28) √43: irrational
29) -2/3: rational
30) 0.27: rational
31) 5/13: rational