Is 0.250 greater or less than 0.375?

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$0.250 < 0.375 \text{ }$ because $\text{ } 0.2 < 0.3$

Explanation:

This is directly comparable with asking

Is $\textcolor{b l u e}{2} 50$ 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.

$\textcolor{b l u e}{2} 00 < \textcolor{b l u e}{3} 00$

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

$0 \textcolor{b l u e}{.2} 50 \mathmr{and} 0 \textcolor{b l u e}{.3} 75$

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

In this case they both show tenths.

$\frac{2}{10} < \frac{3}{10}$, therefore, no matter what digits follow, the first number will be smaller than the second.

Compare the following:

$2 , 386 \mathmr{and} 395 \text{ } \leftarrow$ there are $2$ thousands, so the first number is bigger.

$0 \textcolor{b l u e}{.0} 98 \mathmr{and} 0 \textcolor{b l u e}{.1} 56$

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

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John D. Share
Feb 8, 2018

$0.250$ is less than $0.375$

Explanation:

Start by comparing the digits in the tenths place:

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

$\textcolor{l i g h t g r a y}{0.} \textcolor{red}{2} \textcolor{l i g h t g r a y}{50} \text{ "" "" } \textcolor{l i g h t g r a y}{0.} \textcolor{b l u e}{3} \textcolor{l i g h t g r a y}{75}$

$\textcolor{w h i t e}{\text{---"color(red)2" "" "" "" "color(white)"-..}} \textcolor{b l u e}{3}$

$\textcolor{w h i t e}{\text{---"color(red)2" "" "<" "color(white)"-.}} \textcolor{b l u e}{3}$

Since $\textcolor{red}{2}$ is less than $\textcolor{b l u e}{3}$, $\text{ } \textcolor{red}{0.250}$ is less than $\textcolor{b l u e}{0.375}$.

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