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How many rational numbers are there between $- 1$ and $0$ ?

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Infinite

1000

4990

None

answer is A.

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Detailed Solution

To find the number of rational numbers between two rational numbers.
Let’s take the given number -1 and 0.
Consider

a and b

as rational numbers. Then a rational number

n_{1}

can be find in between

a and b

such that

a < n_{1} < b

using the formula

n_{1} = \frac{a + b}{2}

.
Similarly, again we can find a rational number between

a and n_{1}

and

n_{1} and b

and so on.
Hence, between any two distinct rational numbers there are infinitely many rational numbers.
Hence, there are infinite rational numbers between -1 and 0.
Therefore, option 1 is correct.

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