Question

Which is greater 2 1/4 or 2.1?

Answer 1

`2 1/4`

Explanation:

`2 1/4` is `2.25` which is greater than `2.1`

Answer 2

`2 1/4` is greater than `2.1`.

Explanation:

`2 1/4 = 2+1/4`
`1/4 = 0.25`
`2 + 0.25 = 2.25`
`2.25>2.1`

Answer 3

`2.1color(white)("d") < color(white)("d")2 1/4`

Explanation:

As both numbers 'contain' 2 you can for now forget about the 2's and just concentrate on number parts that are less than 1.

So we are comparing `1/4 and 0.1`

The first decimal place is counting in `10^("ths")` so we are comparing:

`1/4 and 1/10`

The larger the bottom number the 'smaller' is the things that we are counting (top numbers)

As 10 is greater than 4 and the top numbers are the same then `1/10` is 'smaller' than `1/4`

Thus `1/10 <1/4`

So it follows that

`color(white)("dd")ubrace(2 1/10)color(white)("d") < color(white)("d")2 1/4`
`color(white)("d...")darr`
`"Same value"`
`color(white)("d,,,,")uarr`
`color(white)("d,,") obrace(color(white)(.)2.1color(white)(.))color(white)("d") < color(white)("d")2 1/4`