Question

express the following numbers in p/q from : 2.23555555.....​

Answer 1

Answer:

$\frac{503}{225}$

Step-by-step explanation:

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Answer 2

Answer :

2.23555.... = 505/225

Solution :

Here ,

We need to convert 2.23555... in the form of p/q where q ≠ 0 .

Let the given number be X .

Thus ,

X = 2.23555.... --------(1)

Now ,

Multiplying both the sides of eq-(1) by 100 ,

We have ;

=> 100 × X = 100 × 2.23555....

=> 100X = 223.555.... --------(2)

Now ,

Multiplying both the sides of eq-(2) by 10 ,

We have ;

=> 10 × 100X = 10 × 223.555....

=> 1000X = 2235.555.... ----------(3)

Now ,

Subtracting eq-(2) from (3) , we have ;

=> 1000X - 100X = 2235.555... - 223.555...

=> 900X = 2012

=> X = 2012/900

=> X = 503/225

=> 2.23555.... = 505/225

Hence ,

2.23555.... = 505/225