Rational vs Irrational Numbers

Which statement accurately defines a rational number?

• A number that can be written as a ratio of two integers.

• A number whose decimal digits never end.

• A number that cannot be accurately represented as a fraction.

• A number that is always a whole number.

Why can't Pi be represented exactly as a fraction, even though approximations like 22/7 are used?

• Pi is a whole number, not a fraction.

• Fractions can only represent terminating decimals.

• Pi's decimal digits never end and never repeat, making an exact fractional representation impossible.

• Pi is a negative number, and fractions are always positive.

What is a defining characteristic of the decimal digits of an irrational number?

• They always terminate after a finite number of digits.

• They eventually repeat in a predictable pattern.

• They never end and never repeat in a pattern.

• They are always whole numbers.

How can one distinguish between a rational and an irrational number based on their decimal representations?

• Rational numbers have decimal digits that always end, while irrational numbers have digits that go on forever.

• Rational numbers have decimal digits that either end or repeat, while irrational numbers have digits that never end and never repeat.

• Rational numbers have decimal digits that never repeat, while irrational numbers have digits that always repeat.

• Rational numbers are always integers, while irrational numbers are always decimals.

In terms of quantity, how do irrational numbers compare to rational numbers?

• There are fewer irrational numbers than rational numbers.

• There are an equal number of irrational and rational numbers.

• There are infinitely more irrational numbers than rational numbers.

• The quantity of irrational numbers cannot be determined.