Question

Express the rational number 32.434343....in the form p/q, where p and q are integers and q ≠0​

Answer 1

Answer:

3211/99

Step-by-step explanation:

As per the provided information in the given question, we have to express 32.434343.... in the form of p/q where q ≠ 0.

Let us suppose that x = 32.434343.... . 43 is repeating continuously after the decimal point. So, it is a repeating block. Thus,

↠⠀x = 32.434343.... 1)

Now, multiply 100 on both sides.

↠⠀100(x) = 10p(32.434343....)

Performing multiplication on both sides.

↠⠀100x = 3243.4343....2)

Now, subtract the equation ( 1 ) from equation ( 2 ).

↠⠀100x = 3243.4343....

⠀⠀⠀⠀⠀x = ⠀ 32.4343....

⠀_____________________

⠀⠀⠀⠀99x = 3211

⠀_____________________

We get that,

↠⠀99x = 3211

Transposing 99 from LHS to RHS.

↠⠀x = 3211/99

Therefore, we got the required answer. 3211/99 is the p/q form of 32.434343.... .

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