Question

express 2.317317317...... in te form of p/q

Answer 1

Step-by-step explanation:

please refer to the attachment

I hope it would help you

thank you

Answer 2

Answer:

2.317317317...... = $\frac{2315}{999}$

Step-by-step explanation:

Given,

Decimal number is 2.317317317......

Required to express the given decimal number in the form $\frac{p}{q}$

Solution:

Every recurring decimal number is a rational number, and hence every recurring decimal number can be expressed in the form $\frac{p}{q}$

Let 'x' be the given decimal number

x = 2.317317317......  ---------------------(1)

Since there are three recurring decimals, multiply equation (1) by 1000,

1000x = 2.317317317......×1000

1000x = 2317.317317....... -----------------(2)

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

1000x - x = 2317.317317.......-  2.317317317......

999x = 2315

x = $\frac{2315}{999}$

2.317317317...... = $\frac{2315}{999}$

#SPJ2