Question

calculate value of 2.9999..... in p/q form

Answer 1

Concept:

The accepted method for representing both integer and non-integer numbers is the decimal numeral system.

Given:

2.9999.....

To find:

p/q form

Solution:

In this question, we have been provided a decimal number which we have to change to p/q form.

So first, we will assume the number to be x, then we get,

x=2.999..... ----------------1

Now, we will multiply the number with 10

10x=29.9999..... ------------------2

Now, we will subtract equation 2 from equation

$10x-x=29.99..-2.99...\\9x=27\\x=\frac{27}{9} \\x=3$

So, we get the value of x=3

Hence, the p/q form is $\frac{3}{1}$

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