- AInfinitely many
- BExactly one
- CExactly two
- DNone
Step-by-Step Solution
Between any two distinct rational numbers there are infinitely many rational numbers. This is the density property.
Answer: A) Infinitely many
How many rational numbers lie between and ?
Class 7Rational NumbersRational Numbers
Key idea: Rationals on the number line
Every rational number has a place on the number line. Negative rationals on the left of 0, positive on the right. Between any two rationals, you can always find another rational (in fact, infinitely many) — this is called **density**.
Example: between 1/3 and 1/2, the average (1/3 + 1/2)/2 = 5/12 sits in the middle. Between 1/3 and 5/12 there's another rational, and so on, forever.
Example: between 1/3 and 1/2, the average (1/3 + 1/2)/2 = 5/12 sits in the middle. Between 1/3 and 5/12 there's another rational, and so on, forever.
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