Question

Express 0.001001001.... in the form of p/q,where q is not equal to 0

Answer 1

i hope it helped u if yes mark it brainliest and follow me plzzzzzz plzzzzzz plzzzzzz

Answer 2

Answer:

0.001001001.... in the form of p/q is $\frac{1}{999}$where 999 is not equal to 0.

Step-by-step explanation:

Given digit is 0.001001001.....

Here we want to express 0.001001001.... in the form of $\frac{p}{q}$

Let,

$x = 0.001001001......(1)$

Multiplying both side by 1000,we get,

$1000x = 1.001001001.......(2)$

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

$1000x - x = 1.001001001... -0.001001001...$

$999x = 1 \\ x = \frac{1}{999}$

So,

$x = 0.001001001 ...= \frac{1}{999}$

This is a problem of Algebra.

Some important formulas of Algebra,

(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)