Question

prove algebrically that o.o15 can be written as 1/66

Answer 1

Call x = 0.0151515... (i)

Multiply both sides by 100:

100x = 100 * 0.0151515...

100x = 1.5151515...

That can be expressed as this sum:

100x = 1.5 + 0.0151515... (ii)

Now, subtract (i) from (ii):

100x - x = 1.5 + 0.0151515... - 0.0151515..

99x = 1.5

Multiply both sides by 10, so you get rid of decimals:

10 * 99x = 10 * 1.5

990x = 15

Therefore,

x = 15/990

Now, reduce that fraction by dividing both numerator and denominator by gcd(15, 990) = 15, and you finally get

x = (15 : 15)/(990 : 15)

x = 1/66 <----- there it is.

0.0151515... = 1/66

I hope this helps. =)

Answer 2

In this question we need to prove algebraically that 0.015 can be written as 1/66.

According to the question,

Let x be 0.0151515                                                            ... (i)

Multiplying both sides by 100, we get,

$100x = 100 \times 0.0151515...$

100x = 1.5151515...

This above term can be expressed as this sum:

100x = 1.5 + 0.0151515                                                     ... (ii)

Now, subtracting (i) from (ii). We get,

100x - x = 1.5 + 0.0151515... - 0.0151515..

99x = 1.5

Now, multiplying both sides by 10.

We get,

$10 \times 99 x = 10 \times 1.5$

990 x = 15

$x = \dfrac{15}{990}$

  Now, reducing that fraction by dividing both numerator and denominator by gcd (15, 990) = 15, and we get,

$x = \dfrac{15 : 15}{990: 15} \\\\x = \dfrac{1}{66}$    

Therefore,

$0.0151515... = \dfrac{1}{66}$

Hence proved  $0.0151515... = \dfrac{1}{66}$ .

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https://brainly.com/question/19426180