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Is the fraction 1-3 equivalent to a terminating decimal or a decimal that doesn't terminate?
The fraction 1/3 does not terminate.
When a fraction is changed to a decimal and the remainder is not zero a digit or block of digits will eventually start to repeat. such a decimal is called a what?
recurring decimal
What is barnotion?
The line over the digits that repeat in a repeating decimal.
Is it possible to express every decimal as a fraction?
Not all decimals can be expressed as fractions. Only terminating and recurring decimals can be expressed as fractions. eg a recurring decimal: 0.3333333... = 1/3 A terminating decimal: 0.125 = 1/8 A decimal that does not recurr or terminate, cannot be expressed as a fraction. eg Pi = 3.141592654... Pi can not be expressed as a fraction as it does not recurr or terminate. It can only be approximated to a fraction. eg Pi ≈ 355/113 but is correct to 6 decimal places.
How can you predict whether a quotient will be terminating decimal or a repeating decimal?
If the denominator of the fraction, when written in its simplest form, has any prime factor other than 2 or 5 then it will be a repeating decimal fraction otherwise it will terminate.
