QuestionOrder the numbers $2.\overline{3}, \sqrt{8}, 2.5, 2 \frac{1}{4}$ and place them on a number line.

Studdy Solution

STEP 1

Assumptions1. The numbers given are $. \overline{3}, \sqrt{8},.5, \frac{1}{4}$ . We need to compare and order these numbers3. We need to locate each number on a number line

STEP 2

First, we need to understand what each number represents. $2 . \overline{}$ is a repeating decimal that represents the number $2.333...$
$\sqrt{8}$ is the square root of8, which is approximately $2.8284$
$2.5$ is a decimal number $2 \frac{1}{4}$ is a mixed number, which can be converted to a decimal number $2.25$

STEP 3

Now, we can compare these numbers.Clearly, $2 . \overline{3}$ is less than $2.5$ and $\sqrt{8}$ , but greater than $2 \frac{1}{}$ .
$2 \frac{1}{}$ is less than all other numbers.
$2.5$ is less than $\sqrt{8}$ but greater than $2 . \overline{3}$ and $2 \frac{1}{}$ .
$\sqrt{8}$ is greater than all other numbers.

STEP 4

So, the order of the numbers from least to greatest is $2 \frac{1}{4},2 . \overline{3},2., \sqrt{8}$

STEP 5

Now, let's locate these numbers on a number line.First, draw a number line and mark the numbers2 and3.Then, locate the numbers $2 \frac{1}{4}$ , $2 . \overline{3}$ , $2.5$ , and $\sqrt{8}$ on the number line.Remember that $2 \frac{1}{4}$ is just a little more than2, $2 . \overline{3}$ is a little more than $2 \frac{1}{4}$ , $2.5$ is halfway between2 and3, and $\sqrt{8}$ is a little less than3.

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