Question

express the following decimals into rational form (p/q,q=0) f) 2.23444.....
​

Answer 1

Here,

$\tt \large{Decimal = 2.23 \overline{4 }}$

Now,

$\text{Let \: x = 2.23}{ \overline4}$

$100x = 223. \overline{4} \: \: \: \: \: \: \: \: \: \: \: \: \dots \: (1)$

$1000x = 2234. \overline4\: \: \: \: \: \: \: \: \: \: \: \: \dots \: (2)$

Subtracting Equation (1) from (2), we get,

$1000x - 100x = 2234.\overline4 - 223. \overline4 \\ = > 900x =20 11.0 \\ \\ = > \: \: \: \: x = \frac{2011}{900}$

Thus,

$\huge \pink{2.23\overline{444}} = \pink { \frac{2011}{900} }$

Answer 2

Given : 2.23444.......

To Find : express the decimals into rational form

Solution:

2.23444.........

$2.23\overline{4}$

Lat say

$N=2.23\overline{4}$

Multiply by 100

$100N=223.\overline{4}$

Multiply by 1000

$1000N=2234.\overline{4}$

=> 900N = 2011

=> N = 2011/900

$2.23\overline{4}$  =  2011/900

Learn More:

https://brainly.in/question/24108346

Express 1.27 bar on 27 in the form of p/q, where p and q are integers ...

https://brainly.in/question/2457246

express 2.136(bar on 136) in p/q. also write in simplest form ...

https://brainly.in/question/11047507