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Converting Recurring Decimals to Fractions

Number • Fractions, decimals and percentages

Key concepts

What you'll likely be quizzed about

  • A recurring decimal is a decimal fraction in which a digit or group of digits repeats infinitely.
  • For instance, the decimal 0.333...
  • can be expressed as a fraction.
  • Recognizing the repeating section is crucial for conversion.
  • To convert a recurring decimal, identify the repeating part.
  • Define the decimal as 'x'.
  • For example, if x = 0.666..., the repeating part is '6'.
  • Multiply 'x' by a power of ten that matches the length of the repeat, resulting in 10x = 6.666...
  • Subtract the initial 'x' from this equation to eliminate the repeating part.
  • This yields 10x - x = 6.666...
  • - 0.666..., simplifying to 9x = 6.
  • Thus, x = 6/9, which reduces to 2/3.

Flashcards

Test your knowledge with interactive flashcards

How can you simplify the fraction obtained from a recurring decimal?

Click to reveal answer

Divide both the numerator and denominator by their greatest common divisor.

Key notes

Important points to keep in mind

Recognize repeating sections clearly.

Multiply by powers of ten effectively.

Always simplify fractions to their lowest form.

Ensure to subtract equations correctly.

Understand the relationship between decimals and fractions.

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