Question

The average weight of a newborn panda is 0.2, or 2/10 pound. Between what two integers is the weight of a newborn panda?​

Answer 1

`(2)/(10)` lies between 0 and 1.

Explanation:

We must have in mind that given average weight of a newborn panda is a non-integer rational number, such that lies between two integer rational number. In other words, this number must satisfy the following condition:

`n < (a)/(b) < n +1`,
`n, a, b \in \mathbb{N}_(O)`

`\mathbb{N}_(O) = \mathbb{N}\,\cup\,{\{0\}}`

Which is now developed mathematically to deduce a useful expression to find integers:

1)
`n < (a)/(b) < n +1` Given

2)
`n \cdot 1 < (a)/(b) < n\cdot 1 + 1` Modulative property

3)
`n \cdot (b\cdot b^(-1)) < a\cdot b^(-1) < n \cdot (b\cdot b^(-1)) + b\cdot b^(-1)` Existence of Multiplicative inverse/Definition of division.

4)
`(n\cdot b)\cdot b^(-1) < a\cdot b^(-1)< [(n+1)\cdot b] \cdot b^(-1)` Commutative, Associative and Distributive properties.

5)
`n\cdot b < a < (n+1)\cdot b` Compatibility with Multiplication/Existence of Multiplicative Inverse/Modulative Property/Result.

If we know that
`a = 2` and
`b = 10`, the following inequation is formed:

`10\cdot n < 2 < 10\cdot (n+1)`

It is quite evident to conclude that
`(2)/(10)` lies between 0 and 1.