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Flashcards · Maths · Standard Form and Accuracy

Recurring Decimals and Rational Numbers

16 cards

  1. What is a terminating decimal?

    A decimal that stops.

  2. What is a recurring decimal?

    A decimal in which a digit or block of digits repeats for ever.

  3. How are recurring decimals written?

    With dots over the first and last repeating digits.

  4. What is \(\dfrac{1}{3}\) as a decimal?

    \(0.\dot{3}\).

  5. What is \(\dfrac{3}{11}\) as a decimal?

    \(0.\dot{2}\dot{7}\).

  6. What is \(\dfrac{5}{6}\) as a decimal?

    \(0.8\dot{3}\).

  7. When does a fraction give a terminating decimal?

    When the bottom number, in simplest form, has only prime factors 2 and 5.

  8. How do you write \(0.\dot{4}\) as a fraction?

    \(\dfrac{4}{9}\) (Higher tier).

  9. How do you write \(0.\dot{4}\dot{5}\) as a fraction?

    \(\dfrac{5}{11}\) (Higher tier).

  10. What is the first step in converting a recurring decimal?

    Write \(x =\) the decimal.

  11. Why do you multiply by 10, 100 or 1000?

    To line up the repeating digits so they cancel on subtracting.

  12. What is a rational number?

    A number that can be written as a fraction of two integers.

  13. What is an irrational number?

    A number that cannot be written as a fraction.

  14. Is \(\pi\) irrational?

    Yes.

  15. Is \(\sqrt{16}\) rational?

    Yes, it equals 4.

  16. Is \(\sqrt{7}\) rational?

    No, it is irrational.