Question

Express 7.235 bar 235 in p/q form

Answer 1

Given:

A number -

• $\bf \to 7.\overline{235}$

What To Find:

We have to -

• Express in the form of [p/q].

Solution:

• First Method:-

Let's take -

$\bf \to x = 7.\overline{235}$

Can be written as,

$\bf \to x = 7.235235\dots$

Multiply both sides by 10,

$\bf \to 1000x = 7235.235\dots$

Here we have formed -

• $\bf \to x = 7.235235\dots - [1st \: eq.\!]$

• $\bf \to 1000x = 7235.235\dots - [2nd \: eq.\!]$

Subtract 1st eq. from 2nd eq.,

$\bf \to 1000x - x = 7235.235\dots \: - 7.235\dots$

Subtract both sides,

$\bf \to 999x = 7228$

Take 999 to RHS,

$\bf \to x = \dfrac{7228}{999}$

∴ Thus, we have expressed $\bf 7.\overline{235}$ in [p/q] form

• Second Method:-

We know that -

$\bf \to \dfrac{p}{q} \: form = \dfrac{Complete \:no.- No. \: formed \: by \:NRD​}{No.\:of\:9as\:RD\:after\:that\:write\:as\:0\:as\:NRD\:after\:decimal}$

Where -

• $\bf \to NRD = Non-repe{a}ting \: digits$

• $\bf \to RD = Repe{a}ting \: digits$

Substitute,

$\bf \to \dfrac{p}{q} \: form = \dfrac{7235-7}{999}$

Subtract the values,

$\bf \to \dfrac{p}{q} \: form = \dfrac{7228}{999}$

∴ Thus, we have expressed $\bf 7.\overline{235}$ in [p/q] form