Question

Express 3.21 bar bar is upon the 1 and write it in p/q form

Answer 1

$Let \: x = 3.2\bar {1} \: ---(1)$

/* Multiplying equation (1) by 10, we get */

$\implies 10x = 32.\bar{1} \: --(2)$

/* Multiplying equation (2) by 10, we get */

$\implies 100x = 321.\bar{1} \: --(3)$

/* Subtract equation (2) from equation (3), we get */

$\implies 99x = 289$

$\implies x = \frac{289}{99}\: \blue{ ( \frac{p}{q} \: form )}$

Therefore.,

$\red{ 3.2\bar {1}}\green { = \frac{289}{99}\: \blue{ ( \frac{p}{q} \: form )}}$

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Answer 2

x = 3.2111...... (1)

10x = 10 × 3.2111...

10x = 32.111...

10x - x = 32.111.. - 3.2111...

9x = 28.9

x = 289/90. (2)

from (1) and (2)

3.2111... = 289/90