Question

The rational number 0.333... can also be written as *

Answer 1

$Let \: x = 0.3333\cdot\cdot\cdot \: --(1)$

/* Multiplying both sides by 10, we get */

$\implies 10x = 3.3333\cdot\cdot\cdot \: --(2)$

/* Subtract equation (1) from equation (2), we get */

$\implies 10x - x = 3.3333\cdot\cdot\cdot-0.3333\cdot\cdot\cdot$

$\implies 9x = 3$

$\implies x = \frac{3}{9}$

$\implies x = \frac{1}{3}$

Therefore.,

$\red { 0.3333\cdot\cdot\cdot \:can \:be \: written }\\\red {as } \green {= \frac{1}{3}} \\\green { = 0.\overline {3}}$

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