Question

Express 5.1233333..... in p/q
form where p and q are co-primes.​

Answer 1

5.1233333..... =  1537/300

Step-by-step explanation:

Express 5.1233333..... in p/q  form

Let say

N  = 5.1233333......

100N = 512.3333333....

1000N = 5123.333333.....

=> 1000N - 100N = 5123.333333..... - 512.3333333....

=> 900N  = 4611

=> N = 4611/900

=>  N = 1537/300

1537 & 300 are coprime

Hence

5.1233333..... =  1537/300

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Answer 2

5.123333 is expressed as $\dfrac{4611}{900}$.

Step-by-step explanation:

Since we have given that

$x=5.123333...=5.12\bar{3}$

We need to express it in p/q form:

We multiply it my by 10, we get that

$10x=51.2333333$

Now, we will subtract both the equations:

$10x-x=51.23333-5.12333\\\\9x=46.11\\\\x=\dfrac{46.11}{9}\\\\x=\dfrac{4611}{900}$

Hence, 5.123333 is expressed as $\dfrac{4611}{900}$.

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