Question

Express 0.435353535……..… in the form P/q, where p and q are integers and q not zero​

Answer 1

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x = 0.4353535…

100x = 43.53535…

100x = 43 + 0.53535…

100x = 43 + 0.1 + 0.4353535…

100x = 43.1 + x

100x - x = 43.1

99x = 43.1

99x = 431/10

x = 431/990

0.4353535… = 431/990

Hope it's helpful to you ☺️❤️

Answer 2

Step-by-step explanation:

$\bold{Let \: \frac{p}{q} = 0.435353535…}$

Multiplying 10 on both sides,

$10 \frac{p}{q} = 4.35353535… - - - (i)$

Multiplying 1000 on both sides,

$1000 \frac{p}{q} = 435.353535... - - - (ii)$

Subtracting Equation (i) from Equation (ii),

$\scriptsize1000 \frac{p}{q} - 10 \frac{p}{q} = (435.353535...) - (4.353535...)$

$990 \frac{p}{q} = 431$

$\frac{p}{q} = \frac{431}{990}$

I hope it is helpful

Answer 3

Step-by-step explanation:

$\bold{Let \: \frac{p}{q} = 0.435353535…}$

Multiplying 10 on both sides,

$10 \frac{p}{q} = 4.35353535… - - - (i)$

Multiplying 1000 on both sides,

$1000 \frac{p}{q} = 435.353535... - - - (ii)$

Subtracting Equation (i) from Equation (ii),

$\scriptsize1000 \frac{p}{q} - 10 \frac{p}{q} = (435.353535...) - (4.353535...)$

$990 \frac{p}{q} = 431$

$\frac{p}{q} = \frac{431}{990}$

I hope it is helpful

Answer 4

Step-by-step explanation:

$\bold{Let \: \frac{p}{q} = 0.435353535…}$

Multiplying 10 on both sides,

$10 \frac{p}{q} = 4.35353535… - - - (i)$

Multiplying 1000 on both sides,

$1000 \frac{p}{q} = 435.353535... - - - (ii)$

Subtracting Equation (i) from Equation (ii),

$\scriptsize1000 \frac{p}{q} - 10 \frac{p}{q} = (435.353535...) - (4.353535...)$

$990 \frac{p}{q} = 431$

$\frac{p}{q} = \frac{431}{990}$

I hope it is helpful