Question

Is 0.250 more or less than 0.375?

Answer 1

`0.250` is less than `0.375`

Explanation:

Start by comparing the digits in the tenths place:

`color(red)(0. 250)" "" "" "color(blue)(0. 375`

`color(lightgray)(0.)color(red)2color(lightgray)50 " "" "" "color(lightgray)(0.)color(blue)3color(lightgray)75`

`color(white)"---"color(red)2" "" "" "" "color(white)"-.."color(blue)3`

`color(white)"---"color(red)2" "" "<" "color(white)"-."color(blue)3`

Since `color(red)2` is less than `color(blue)3`, `" "color(red)0.250` is less than `color(blue)0.375`.

Answer 2

`0.250 < 0.375" "` because `" "0.2 <0.3`

Explanation:

This is directly comparable with asking

Is `color(blue)(2)50` greater than or less than `color(blue)(3)75?`

The most important place holders are the first ones.

In this case they both show hundreds.

`color(blue)(2)00 < color(blue)(3)00`

In the case of the decimals, we use the same approach,

`0color(blue)(.2)50 and 0color(blue)(.3)75`

The most important place holders are the first ones which are not `0`

In this case they both show tenths.

`2/10 < 3/10`, therefore, no matter what digits follow, the first number will be smaller than the second.

Compare the following:

`2,386 and 395" "larr` there are `2` thousands, so the first number is bigger.

`0color(blue)(.0)98 and 0color(blue)(.1)56`

You are comparing `0` tenths with `1` tenth, so the second number is bigger.