1. CONVERTING RECURRING DECIMALS INTO FRACTIONS

2. 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

3. 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 =

4. 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

5. 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

6. Some Questions To Try Convert 0.156156156156 to a fraction
Remember: Always cancel the fraction down by Common Factors if possible.

7. 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.

8. 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.