Non-Terminating Non-Repeating Decimals
A non-terminating non-repeating decimal is a decimal that goes on forever without a repeating block of digits, and it represents an irrational number.
Practice This ConceptMain explanation
Teacher explanation
Such decimals cannot be written exactly as p/q. This is the key decimal test used to distinguish irrational numbers from repeating rational decimals.
Example
√2 = 1.4142135... and π = 3.14159... are non-terminating non-repeating decimals, so they are irrational.
Simple analogy
Repeating means rational; no repeat means irrational.
Common confusion
Students may see a long decimal and call it irrational even when a repeating pattern is present.
Exam tip
Look for a fixed repeated block. If a block repeats forever, the decimal is rational; if no block repeats and it does not terminate, it is irrational.
Answer writing and exam use
1-mark use
Write the exact meaning of non-terminating non-repeating decimals in one clean line.
2-mark use
Define non-terminating non-repeating decimals and add one example or condition.
3-mark use
Explain non-terminating non-repeating decimals, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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