Question

Express 2.45454545........in the form of p/q

Answer 1

Step-by-step explanation:

let,

x=2.454545...

100x=245.4545....—————1

10000x=24545.45.....————2

Now,

Equation- 2-1

10000x=24545.45...

-100x=245.45...

—————————————

9900x=24300.00....

x=24300/9900

x=27/11

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Answer 2

Answer:

2.45454545........in the form of p/q is 27/11.

Step-by-step explanation:

Given number is 2.45454545....

Let,

$x = 2.45454545.......(1)$

We are multiplying equation (1) by 100,

$100 \times x = 245.4545....(2)$

and we are multiplying equation (1) by 1000,

$10000 \times x = 24545.45.....(3)$

We are subtracting equation (3) from (2)

$10000x - 100x = 24545.45.. - 245.45... \\ 9900x = 24300 \\ x = \frac{24300}{9900} \\ x = \frac{243}{99} \\ x = \frac{27}{11}$

So,

$2.454545..... = \frac{27}{11}$

So, required p/q form is 27/11.

This is a problem of numbers part of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

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