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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.
If the decimal doesn't terminate or repeat is is it a rational number still or not?
Not.
Are decimals that do NOT terminate or repeat?
Decimals can either terminate OR repeat. One decimal does not do both. Example-- 3.059 is a terminating decimal, meaning it stops. Example-- 3.059059... is a repeating decimal, meaning it repeats. You would write that as 3.059 with a line over the 0,5, and 9 because they repeat themselves.
Are decimals rational?
Some are, some aren't.If the portion after the decimal point:terminates (eg 0.125);does not terminate, but repeats one or more digits (eg 0.333..., 0.181818...)does not terminate, but has one or more digits followed by one or more further digits that repeat (eg 0.16666..., 0.258373737...)then the decimal is rational.otherwise, if the decimal does not terminate and does not repeat any digits (eg π = 3.1415726..., √2 = 1.41421...)then the decimal is irrational (not rational).
If it doesn if a decimal doesn't terminate or repeat is it still a rational number or not?
No, if a decimal does not terminate or repeat, it is not a rational number. Rational numbers can be expressed as a ratio of two integers, and their decimal representation either terminates or repeats after a certain point. Decimals that do not have a pattern and continue indefinitely are considered irrational numbers.
What is the difference between the decimal expansion in irrational and rational numbers?
Decimals that terminate or repeat in some fashion are rational, while decimals that expand forever are irrational.
How do we determine whether the decimal representation of a quotient of two integers with the divisor not equal to zero will terminate or repeat?
It the divisor has any prime factor other than 2 or 5 [prime factors of 10], then the quotient will repeat. Otherwise it will terminate.
Is 17.1 rational?
Yes. Any number that can be expressed as a finite or repeating decimal is a rational number. Irrational numbers have decimal expansions that neither repeat nor terminate.
Is the fraction 1-3 equivalent to a terminating decimal or a decimal that doesn't terminate?
The fraction 1/3 does not terminate.
Is every rational number a decimal number?
All real numbers have a decimal representation. Rational numbers have decimal representations that terminate or repeat infinitely. Irrational numbers have decimal representations that are non-terminating and non-repeating.
Does an irrational number terminate?
Its decimal representation does not terminate.
Can a number both repeat and terminate?
No.
Is the fraction 13 equivalent to a terminating decimal or a decimal that does not terminate?
1/3 does not terminate.
