Question

How do you order the following from least to greatest without a calculator `3, sqrt10, 3/4, -1.5`?

Answer 1

The order of the numbers (from least to greatest) would be `-1.5, 3/4,3, and sqrt10`.

Explanation:

First, start by converting all numbers into decimals.
Thus...

`3` would be `3` (it's fine as it is; you could also express it as 3.0 to emphasize).

`sqrt10` would become approximately `3.2` (which squared would equal `10.24`; you can figure this out without a calculator and you can also easily figure out this is greater than `3` because `3^2` equals `9` so, `sqrt10` would have to be a bit greater.

`3/4` would become `0.75` (divide numerator by denominator).

`-1.5` would be `-1.5` (it's already in decimal form so, you don't really have to do anything to it).

To conclude, look at their sign (whether it's positive or negative). In addition, the smallest value would have to be `-1.5` (it's negative, thus, it has a smaller value).

Then, look at their place values. In this case, `0.75` was the `2nd` smallest value (look at the ones place). After that, do the same thing so, that `3` would go next and finally `sqrt10`.

Short notice: If by any chance you have to list any numbers on a number line and you changed them into another number so that you could order them more easily, be sure to change them back to their original form for your final answer.