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Published byJayden Saxton Modified about 1 year ago

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CONVERTING RECURRING DECIMALS INTO FRACTIONS

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Rational and Irrational Numbers Rational Numbers 1)A Whole Number 2)A Fraction 3)Repeating Decimal e.g. 2.345234523452... Irrational Numbers 1)Never-ending non-repeating decimals e.g 5.878945672341098094530320745328... 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 2 2 (4) and 3 2 (9). The square roots of 1,2,3,5,6,7,8,10 are Irrational. e.g. Square root of 3 = 1.7320508....

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Recurring Decimals Are Fractions Recurring decimals are fractions in disguise ! Method 1)Find the length of the repeating sequence. 2)Continue to multiply by 10 until one whole repeating sequence is on the left of the decimal point. 3) Subtract the original number from the new multiplied number........Lets do an example

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Example of Recurring Decimal to Fraction Convert 0.624624624624... into a fraction 1)Identify the repeating sequence as 624 2)Multiply by 10 until one 624 sequence is on the left of the decimal point e.g. (x 1000 gives..) 624.624624624624624 3)Subtract 1000x – x = 624.624... – 0.624.. 999x = 624 so the fraction is 624 / 999 cancels to 208 / 333

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Some Questions To Try 1)Convert 0.156156156156 to a fraction 2)Convert 0.123412341234... 3)Convert 0.987698769876... Remember: Always cancel the fraction down by Common Factors if possible.

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Answers 1)Convert 0.156156156156 to a fraction 156/999 = 52/333 (Common Factor = 3) 1)Convert 0.123412341234... 1234/9999 1)Convert 0.987698769876... 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. 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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