Coursework Notes - Number

Decimals

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.

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

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.

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

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

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

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