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Coursework Notes - Number




[ non-recurring decimal to fraction ][ recurring decimal to fraction ]



Terminating decimals All terminating decimals end with one number.


examples: 0.123,  5.61219,  0.00187


They are rational numbers. Remember the definition of a rational number is one that can be expressed as a fraction.



Recurring Decimals - These decimals have number patterns that repeat themselves.


recurring decimals



Converting a fraction to a decimal - Simply divide the numerator by the denominator.


fractions to decimals



Converting a non-recurring decimal to a fraction - First, write out the decimal as a fraction of powers of ten eg 10 ths, 100 ths or 1000 ths. Then just cancel the fraction to its smallest factors.


decimals to fractions



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Converting a recurring decimal to a fraction


  • Multiply the recurring decimal by 10 if 1 decimal place(100 for 2 d.p., 1000 for 3 d.p. etc.).

  • Subtract the recurring decimal.

  • Rearrange the equation to make the recurring decimal the subject.


example #1 - make 0.55555... into a fraction


recurring decimal to fraction #1





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example #2 - make 0.75757575... into a fraction


recurring decimal to fraction #2





example #3 - make 0.692692692... into a fraction

recurring decimal to fraction #3


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