Fractions and Recurring Decimals (Edexcel GCSE Maths): Flashcards
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12 cards from this deck
Definition of recurring decimal
Definition of recurring decimal
A decimal with a pattern that repeats forever
Definition of terminating decimal
Definition of terminating decimal
A finite decimal that comes to an end
When does a fraction give a terminating decimal?
When does a fraction give a terminating decimal?
When the denominator only has prime factors 2 and/or 5
When does a fraction give a recurring decimal?
When does a fraction give a recurring decimal?
When the denominator has prime factors other than 2 and 5
Example: rac{1}{3} as decimal
Example: rac{1}{3} as decimal
(recurring)
Example: rac{1}{2} as decimal
Example: rac{1}{2} as decimal
(terminating)
Why do only 2 and 5 give terminating decimals?
Why do only 2 and 5 give terminating decimals?
Decimal system based on powers of 10, and
Step 1: converting recurring decimal to fraction
Step 1: converting recurring decimal to fraction
Let equal the recurring decimal
Step 2: basic recurring decimal method
Step 2: basic recurring decimal method
Multiply by power of 10 to move past one complete repetition
Quick method: recurring decimal to fraction
Quick method: recurring decimal to fraction
Recurring part on top, same number of 9s on bottom
Method 1: fraction to recurring decimal
Method 1: fraction to recurring decimal
Find equivalent fraction with 9s in denominator
Method 2: fraction to recurring decimal
Method 2: fraction to recurring decimal
Use long division