Question

Express 0.4323232… in the form p/q, where p and q are integers and q ≠ 0.

Answer 1

Answer:

42.8/99

Step-by-step explanation:

hi how is the answer

Answer 2

Answer:

0.4323232… in the form of p/q is $\dfrac{214}{495}$.

Step-by-step explanation:

Given a number, 0.4323232…

This number is non-terminating recurring decimal.

A non-terminating recurring decimal is a decimal that will never end and, one or more numbers after the decimal point will be repeated.

To convert the given decimal to a fraction,

Let $x = 0.4323232...$

Since there is only one digit which is not repeating, therefore multiplying $x$ with 10 on both sides, we get

$10x = 4.323232...$

The recurring part in $x$ is $\overline{32}$.

Two digits are repeating and one digit i.e., 4 is there before them, so totally 3 digits.

Therefore, now multiply $x$ with 1000 on both sides,

$1000x = 432.3232...$

The objective of multiplying with powers of 10 is to get an integer, so that the two numbers have the same numbers after the decimal.

$1000x - 10x = 432.323232...-4.323232...$

$~~~~~~~~~~990x = 432.323232...\\~~~~~~~~~~~~~~~~~~~~~~\underline{-4.323232...}\\~~~~~~~~~~~~~~~~~~~~~428.000000$

$\implies 990x = 428$

$\implies x = \dfrac{428}{990} =\dfrac{214}{495}$

$\therefore 0.4323232$ is equivalent to $\dfrac{214}{495}$

Therefore, 0.4323232… in the form of p/q is $\dfrac{214}{495}$.