Question

Write three rational numbers that lie between the two given numbers.

0, `(-3)/4`

Answer 1

The given numbers are `0, (-3)/4`

Let us convert each of the given numbers into fractions with equal denominators.

0 = `(0 xx 8)/(1 xx 8) = 0/8`

`(-3)/4 = (-3xx2)/(4xx2) = (-6)/8`

We know that,

-6 < -5 < -4 < -3 < -2 < -1 < 0

`therefore (-6)/8 < (-5)/8 < (-4)/8 < (-3)/8 < (-2)/8 < (-1)/8 < 0/8`

`=> (-3)/4 < (-5)/8 < (-4)/8 < (-3)/8 <(-2)/8 < (-1)/8 < 0`

Hence, 3 rational numbers between `(-3)/4`  and 0 are:

`(-5)/8, (-2)/8` and `(-1)/8`