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Yes; by the definition of an irrational number (a number with an infinite amount of changing decimal digits as the number grows minutely larger), the converse is true about rational numbers

a rational number like (1/3) [0.33333333...] can be notated with a bar over any of the digits to notate a repeating decimal digit.

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If the decimal ever ends, or if it never ends but eventually

settles into a repeating pattern of digits, then it can.

Q: Can all rational numbers be written as decimal numbers?

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Yes, all rational numbers can be written as decimal numbers.

Decimal numbers that can be expressed as fractions are rational but decimal numbers that can't be expressed as factions are irrational

All terminating decimal numbers are rational.

They can. And if you include repeating 0s and repeating 9s, then all rational numbers can be written with infinitely long repeating digits.

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.

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Yes, all rational numbers can be written as decimal numbers.

Decimal numbers that can be expressed as fractions are rational but decimal numbers that can't be expressed as factions are irrational

Yes.

All terminating decimal numbers are rational.

They can. And if you include repeating 0s and repeating 9s, then all rational numbers can be written with infinitely long repeating digits.

All repeating decimals are rational numbers. Not all rational numbers are repeating decimals.

because not all rational numbers are integers, recurring numbers, numbers to 1 decimal place and fractions are rational as well but all integers are rational

Yes. Rational numbers are numbers that can be written as a fraction. All rationals are real.

No, it does not.

all rational numbers can be written as fractions. That is the definition of rational numbers.

No. Rational numbers are numbers that can be written as a fraction. All rational numbers are real.

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.