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**CONVERTING RECURRING DECIMALS INTO FRACTIONS**

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**Rational and Irrational Numbers**

A Whole Number A Fraction Repeating Decimal e.g Irrational Numbers Never-ending non-repeating decimals e.g 2) Cannot be expressed as a fraction

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**Square Roots and Cube Roots**

A good source of Irrational Numbers are square and cube roots. Example If you take square roots between 1 and 10 there are 2 Rational square roots 22 (4) and 32 (9). The square roots of 1,2,3,5,6,7,8,10 are Irrational. e.g. Square root of 3 =

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**Recurring Decimals Are Fractions**

Recurring decimals are fractions in disguise ! Method Find the length of the repeating sequence. Continue to multiply by 10 until one whole repeating sequence is on the left of the decimal point. Subtract the original number from the new multiplied number Lets do an example

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**Example of Recurring Decimal to Fraction**

Convert into a fraction Identify the repeating sequence as 624 Multiply by 10 until one 624 sequence is on the left of the decimal point e.g. (x 1000 gives ..) Subtract 1000x – x = – 999x = 624 so the fraction is 624 / 999 cancels to 208 / 333

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**Some Questions To Try Convert 0.156156156156 to a fraction**

Remember: Always cancel the fraction down by Common Factors if possible.

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**Answers Convert 0.156156156156 to a fraction**

156/999 = 52/333 (Common Factor = 3) Convert 1234/9999 Convert 9876/9999 = 3292/3333 (CF = 3) Remember: Always cancel the fraction down by Common Factors if possible.

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SUMMARY Numbers can be Rational or Irrational. Rational numbers are integers or fractions. Recurring Decimals are fractions in disguise and so are also Rational Numbers. All Recurring Decimals are Rational Numbers so can ALWAYS be converted to a fraction.

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The Real Number System. Whole numbers Whole numbers Rational numbers Whole numbers Natural numbers Integers 4 9 15 0 1/2 -8 -3 0.45 -¾ 18% π √2√2 − -5.368257….

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