Question

Express 1.8181.......in the form of p/q where p&q are integers and q is not 0

Answer 1

Answer: 180/99

Step-by-step explanation:

X = 1.818181... - 1

100x = 181.818181... - 2

Subtracting equation 1 from equation 2

100x - x = 181.8181... - 1.8181

99x = 180

x = 180 / 99

Answer 2

Answer:

1.8181.....  = $\frac{20}{11}$

Step-by-step explanation:

Given,

Decimal number 1.8181.....

To find,

Express the given decimal number in the form $\frac{p}{q}$, where p and q are integers and q ≠0

Solution:

Let x = 1.8181..... --------------(1)

Since, there are two recurring decimals, let us multiply the equation with 10² = 100

100x = 100 × 1.8181.....

100x = 181.8181........ -----------(2)

(2) - (1) → 100x - x = 181.8181....... - 1.8181.....

99x = 180

x = $\frac{180}{99}$

= $\frac{20}{11}$

∴x = $\frac{20}{11}$

1.8181.....  = $\frac{20}{11}$

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