Terminating decimal expansion
A fraction in lowest form has a terminating decimal expansion only when its denominator has prime factors 2 and/or 5 and no other prime factors.
Practice This ConceptMain explanation
Teacher explanation
A decimal stops when the denominator can be turned into a power of 10 by multiplying only by 2s or 5s. That is why denominators like 8, 20, 40, 125, and 200 can produce terminating decimals after simplification.
Example
3/8 = 0.375 because 8 = 2^3.
Simple analogy
Only 2 and 5 can make ten.
Common confusion
Students check the original denominator without first reducing the fraction to lowest form.
Exam tip
Always simplify the fraction first, then inspect only the denominator's prime factors.
Answer writing and exam use
1-mark use
Write the exact meaning of terminating decimal expansion in one clean line.
2-mark use
Define terminating decimal expansion and add one example or condition.
3-mark use
Explain terminating decimal expansion, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
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