Q: Why not all the decimal numbers can be written as rational numbers?

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

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.

Yes. any fraction or decimal is a rational number, not an integer.

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

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.

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

No, it does not.

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

Zero is a rational number. Rational numbers are numbers that can be represented by the division of two integers. Zero is zero divided by anything besides zero, so zero is rational.

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.