Question

show that 1.4191919can be expresed in the form of p/q &q is not equal to 0

Answer 1

$<b>Heya mate. (^_-). Solution below.$
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$<u>Your Question -</u>$

Show that 1.4191919... can be expressed in the form p/q where q is not equal to zero.

$<u>Solution -</u>$

Let x = 1.4191919... $\mathcal{(Equation\: i)}$


Then, multiplying both sides by 10, we get

10 × x = 10 × 1.4191919...
=> 10x = 14.191919... $\mathcal{(Equation\: ii)}$


Now, multiplying both sides by 100, we get

100 × 10x = 100 × 14.191919...
=> 1000x = 1419.191919....$\mathcal{(Equation\: iii)}$


Now, subtracting equation ii from equation iii, we get,

1000x - 10x = 1419.191919.. - 14.191919...
=> 990x = 1405
=> x = 1405/990

$\mathfrak{Hence \:proved}$

$<marquee>Therefore, 1.4191919.. = 1405/990.</marquee>$
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Thank you... ;-)