Question

change it into p/q form​

Answer 1

Expressing x = $2.57\overline{5}$ in the p/q form.

Now,

x = 2.57555555........ (i)

By multiplying 100 to both the sides of the equation (i) we get,

100x = 257.55555........ (ii)

Now,

Again multiplying 10 to both the sides of the equation (ii) we get,

1000x = 2575.55555....... (iii)

• Now, subtracting equation (ii) from equation (iii) we get,

1000x = 2575.55555....... (iii)

- 100x  =   257.55555........ (ii)

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900x = 2318.00000........

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So,

⇒ 900x = 2318

⇒ x = 2318/900

[By dividing both the numerator and denominator by 2 we get]

⇒ x = 1159/450

Hence,

• p/q form of $2.57555555...... =\boxed{ \frac{1159}{450}}$

Answer 2

$\huge{\boxed{\sf QuEsTIoN}}$

Express x = 2.575bar in p/q form

$\huge{\boxed{\sf Solution}}$

➳ x = 2.5755555.......(1)

➳ 100x = 257.5555555 .....(2)

➳ 100x = 275.55555555

- x = 2.57555555

99x = 272.98000000

➳ x = 273/99

➳ x = 91/33

★ Hence Verified