Decimal Expansions of Rational Numbers
Learning Objective
I can explain how rational numbers have decimal expansions that terminate or repeat.
Key Concepts
Rational numbers can be expressed as either terminating decimals or non-terminating recurring decimals.
To determine if a fraction will result in a terminating or non-terminating decimal, reduce the denominator to its prime factors.
If the prime factors of the denominator are only 2 or 5, the decimal will terminate; otherwise, it will be a non-terminating recurring decimal.
Practice Questions
This lesson includes 12 practice questions to reinforce learning.
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1. What are the two possible types of decimal expansions for rational numbers?
2. Express the number 7/8 as a decimal. Is it terminating or non-terminating recurring?
3. Without performing division, how can you determine whether the fraction 3/16 will result in a terminating or non-terminating recurring decimal?
...and 9 more questions
Educational Video
Trick to Identify Terminating Rational Numbers & Non-Terminating Recurring Decimals | Don't Memorise
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