Math Problem Statement
Which of the following are irrational numbers?
Solution
The question asks, "Which of the following are irrational numbers?"
Let's analyze the options:
- π (pi): This is an irrational number because it cannot be expressed as a simple fraction. Its decimal expansion is non-repeating and infinite.
- 9.69̅ (repeating 9.69): This is a rational number. A repeating decimal can be converted into a fraction, so it is not irrational.
- 4: This is a whole number, which can be written as a fraction (4/1), making it a rational number.
- 0: This is a rational number, as it can be expressed as the fraction 0/1.
Thus, the only irrational number in this list is π.
Would you like more details, or have any other questions?
Here are 5 related questions to expand your understanding:
- What makes a number irrational?
- Can the square root of any number be irrational?
- Are there other famous irrational numbers like π?
- What is the difference between rational and irrational numbers in terms of decimals?
- How can repeating decimals always be converted to fractions?
Tip: A repeating decimal is always a rational number because it can be written as a ratio of two integers.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Irrational Numbers
Rational Numbers
Formulas
-
Theorems
Irrational numbers cannot be expressed as a ratio of two integers
Repeating decimals are rational
Suitable Grade Level
Grades 6-8