For each number, circle the subset(s) of the real numbers that the number belong to.
26) sqrt(49)
rational, integers, whole numbers, natural numbers, irrational
rational, integers, whole numbers, natural numbers, irrational
rational, integers, whole numbers, natural numbers, irrational
rational, integers, whole numbers, natural numbers, irrational
rational, integers, whole numbers, natural numbers, irrational
rational, integers, whole numbers, natural numbers, irrational
27) - sqrt(81)
28) sqrt(43)
29) - 2/3
30) 0.27
31) 5/12
26) sqrt(49): rational, integers, whole numbers, natural numbers
27) - sqrt(81): rational, integers, whole numbers, natural numbers
28) sqrt(43): irrational
29) - 2/3: rational
30) 0.27: rational
31) 5/12: rational
26) sqrt(49)
- The number sqrt(49) is 7.
- It belongs to the subset of real numbers that are rational, integers, whole numbers, and natural numbers.
27) - sqrt(81)
- The number - sqrt(81) is -9.
- It belongs to the subset of real numbers that are rational, integers, and whole numbers.
28) sqrt(43)
- The number sqrt(43) is an irrational number.
- It belongs to the subset of real numbers that are irrational.
29) - 2/3
- The number -2/3 is a rational number.
- It belongs to the subset of real numbers that are rational.
30) 0.27
- The number 0.27 is a rational number.
- It belongs to the subset of real numbers that are rational.
31) 5/12
- The number 5/12 is a rational number.
- It belongs to the subset of real numbers that are rational.
To determine which subsets of the real numbers a given number belongs to, you need to understand the definitions of these subsets.
1) Rational numbers: These are numbers that can be expressed as a fraction of two integers. For example, 3/4 is a rational number.
2) Integers: These are whole numbers (positive, negative, or zero) and their negatives. For example, -5, 0, and 7 are integers.
3) Whole numbers: These are positive integers, including zero. For example, 0, 1, 2, 3, and so on.
4) Natural numbers: These are positive integers, excluding zero. For example, 1, 2, 3, and so on.
5) Irrational numbers: These are numbers that cannot be expressed as a fraction and have an infinite decimal representation. For example, π (pi) and √2 (square root of 2) are irrational numbers.
Now, let's evaluate each number:
26) √49: The square root of 49 is 7, which is a whole number and a natural number. So, circle whole numbers and natural numbers.
27) -√81: The negative square root of 81 is -9, which is an integer. So, circle integers.
28) √43: The square root of 43 is an irrational number. So, circle irrational.
29) -2/3: This is a fractional number, so it is a rational number. Circle rational.
30) 0.27: This is a decimal number, which can be expressed as a fraction (27/100). It is a rational number. Circle rational.
31) 5/12: This is a fractional number, so it is a rational number. Circle rational.
So, the circles for each number are as follows:
26) Whole numbers, natural numbers
27) Integers
28) Irrational
29) Rational
30) Rational
31) Rational