Question

Express 1.3232323... in the form p/q
where p and q are integers q≠0 .

Answer 1

Answer:

131/99

Step-by-step explanation:

As per the provided information in the given question, we have been asked to express $\sf 1.\overline{32}$ in the form p/q , where p and q are integers q ≠ 0 .

Basically we are asked to write it as a rational number. ❝ Rational number are those numbers which can pe written in the ratio of two integers. For iñstànce, it can be written in the form of p/q , where p and q are integers q ≠ 0 . Rational numbers are represented by Q. ❞

Let us say, $\sf x = 1.\overline{32}$

So, x = 1.3232323$\dots$

Let this be the equation ( 1 ).

Now, multiply 100 on the both sides, i.e in LHS and RHS.

➝ 10(x) = 10(1.3232323$\dots$)

Performing multiplication in the both RHS and LHS.

➝ 10x = 132.323232_(Equation 2)

Now, subtract equation 1 from equation 2.

$\boxed{ \begin{array}{cc} \\ \: \: \: \: \: \: \: \sf{100x = 132.323232 \dots} \\ - \: \: \: \: \: \: \: \: \sf{x =1.32323232 \dots} \\ \boxed{ \: \: \: \: \: \: \: \: \: \: \sf99x = 131 \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \end{array}}$

We get that,

➝ 99x = 131

Transposing 9 from L.HS to R.H.S.

➝ x = 131/99

Therefore, the value of x in the form of p/q is 131/99.