(a) sqrt(23) (b) sqrt(9) (c) (10/21)
(d) (12/4) (e) 58 (f) −33 (g) 0
From the list above, determine the corresponding letters of the numbers that are
(a) whole:
(b) integers:
(c) rational:
whole: bdeg
integer: bdefg
rational: bcdefg
To determine the corresponding letters of the numbers that are whole, integers, and rational, let's break down each concept:
a) Whole numbers are non-negative numbers without any decimals or fractions. They include all natural numbers (positive integers) and zero.
Looking at the list:
(a) sqrt(23) - This is not a whole number as it is positive and contains a square root symbol.
(b) sqrt(9) - This is a whole number because the square root of 9 is 3, and 3 is a whole number.
(c) (10/21) - This is not a whole number as it is a fraction.
(d) (12/4) - This is not a whole number as it is a fraction.
(e) 58 - This is a whole number as it is a positive integer with no decimal or fractional part.
(f) -33 - This is not a whole number as it is negative.
(g) 0 - This is a whole number as it is non-negative and has no decimal or fractional part.
Therefore, the corresponding letters for whole numbers are: b and g.
Now let's move on to integers:
Integers are whole numbers (positive and negative) as well as zero.
Looking at the list:
(a) sqrt(23) - This is not an integer as it is positive and contains a square root symbol.
(b) sqrt(9) - This is an integer as the square root of 9 is 3, which is a whole number.
(c) (10/21) - This is not an integer as it is a fraction.
(d) (12/4) - This is not an integer as it is a fraction.
(e) 58 - This is an integer as it is a positive whole number.
(f) -33 - This is an integer as it is a negative whole number.
(g) 0 - This is an integer as it is neither positive nor negative.
Therefore, the corresponding letters for integers are: b, e, f, and g.
Lastly, let's determine which numbers are rational:
Rational numbers are numbers that can be expressed as a fraction or a ratio of two integers, where the denominator is not zero.
Looking at the list:
(a) sqrt(23) - This is not a rational number as it cannot be expressed as a fraction.
(b) sqrt(9) - This is a rational number as the square root of 9 is 3, which can be expressed as 3/1.
(c) (10/21) - This is a rational number as it is already expressed as a fraction.
(d) (12/4) - This is a rational number as it is already expressed as a fraction.
(e) 58 - This is a rational number as it can be expressed as 58/1.
(f) -33 - This is a rational number as it can be expressed as -33/1.
(g) 0 - This is a rational number as it can be expressed as 0/1.
Therefore, the corresponding letters for rational numbers are: b, c, d, e, f, and g.