Q: A number that connot be expressed as a ratio of two integers or as a repeating or terminating decimal?

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Irrational numbers are numbers that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal.

Yes. 5.0 (a terminating decimal) can be expressed as 4.9999... (a repeating decimal) That may be hard to believe but it is true, as proved by Georg Cantor.

When expressed as a decimal, a rational number will either be terminating (end with a finite number of digits) or repeating (have a repeating pattern of digits).

The latter which would be an irrational number that cannot be expressed as a fraction.

Because terminating or repeating decimals can be written as the quotient of two integers a/b, where b is not equal to zero.

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Rational numbers can be expressed as a terminating or repeating decimal.

Irrational numbers are numbers that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal.

Yes, they are and that is because any terminating or repeating decimal can be expressed in the form of a ratio, p/q where p and q are integers and q is non-zero.

Yes. 5.0 (a terminating decimal) can be expressed as 4.9999... (a repeating decimal) That may be hard to believe but it is true, as proved by Georg Cantor.

They are rational numbers

When expressed as a decimal, a rational number will either be terminating (end with a finite number of digits) or repeating (have a repeating pattern of digits).

If the decimal is terminating or repeating then it can be written as a fraction. Decimal representations which are non-terminating and non-repeating cannot be expressed as a fraction.

An irrational number.

The latter which would be an irrational number that cannot be expressed as a fraction.

Because terminating or repeating decimals can be written as the quotient of two integers a/b, where b is not equal to zero.

No, the sum of a repeating decimal and a terminating decimal is never a terminating decimal.

fractions or decimals