Question

llowing number.
2.4444...
oints
t apply.
☐ irrational number ☐ rational number
☐ integer ☐ whole number
☐ natural number

Explanation:

Step1: Recall number definitions

• Natural Numbers: Positive integers (1, 2, 3, ...). \(2.4444...\) is not an integer, so not natural.
• Whole Numbers: Non - negative integers (0, 1, 2, ...). \(2.4444...\) is not an integer, so not whole.
• Integers: ..., -2, -1, 0, 1, 2, ... \(2.4444...\) has a decimal part, so not an integer.
• Irrational Numbers: Numbers that cannot be expressed as \(\frac{p}{q}\) (\(p,q\) integers, \(q

eq0\)) and have non - repeating, non - terminating decimals. \(2.4444...\) has a repeating decimal (4 repeats), so not irrational.

• Rational Numbers: Numbers that can be expressed as \(\frac{p}{q}\) (\(p,q\) integers, \(q

eq0\)). Let \(x = 2.4444...\)

Step2: Convert repeating decimal to fraction

Multiply \(x\) by 10: \(10x=24.4444...\)
Subtract \(x\) from \(10x\): \(10x - x=24.4444...-2.4444...\)
\(9x = 22\), so \(x=\frac{22}{9}\), which is in the form \(\frac{p}{q}\) (\(p = 22\), \(q = 9\), integers, \(q
eq0\)). So \(2.4444...\) is a rational number.

Answer:

Rational Number (and uncheck Irrational Number, Integer, Whole Number, Natural Number)