Question

Order these numbers from least to greatest.

86
4
17'
20'
-√18,
-
0.25

Answer 1

`-(86)/(20) \quad -√(18) \quad (4)/(17) \quad 0.25`

Explanation:

Negative numbers are always the least

So
`- √(18) = - √(9 \cdot 2) = - 3√(2) \\\\√(2) \approx 1.414\\\\-√(18)= -3 * 1.414 = -4.242`

`-(86)/(20) =- 4.3`

`-4.3 < - 4.242`

or

`-(86)/(20) < -√(18)`

(for negative numbers the larger the value after the negative sign, the smaller it is

We can write 0.25 as 1/4 or 4/16

4/17 has a larger denominator than 4/16 and the larger the denominator for the same numerator the smaller the value is

So 4/17 < 4/16 or 4/17 < 0.25

Therefore from smallest to largest the numbers can be ordered as

`-(86)/(20) \quad -√(18) \quad (4)/(17) \quad 0.25`