2Rational and Irrational Numbers A Whole NumberA FractionRepeating Decimal e.gIrrational NumbersNever-ending non-repeating decimalse.g2) Cannot be expressed as a fraction
3Square 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 =
4Recurring Decimals Are Fractions Recurring decimals are fractions in disguise !MethodFind 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
5Example of Recurring Decimal to Fraction Convert into a fractionIdentify the repeating sequence as 624Multiply by 10 until one 624 sequence is on the left of the decimal pointe.g. (x 1000 gives ..)Subtract 1000x – x = –999x = 624 so the fraction is 624 / 999cancels to 208 / 333
6Some Questions To Try Convert 0.156156156156 to a fraction Remember: Always cancel the fraction down by Common Factors if possible.
7Answers Convert 0.156156156156 to a fraction 156/999 = 52/333 (Common Factor = 3)Convert1234/9999Convert9876/9999 = 3292/3333 (CF = 3)Remember: Always cancel the fraction down by Common Factors if possible.
8SUMMARYNumbers 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.