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Express each of the following decimals in the form $\frac{p}{q}$:
\( 4. \overline{7} \)
Given:
The given decimal number is \( 4 . \overline{7} \).
To do:
We have to express the given decimal in $\frac{p}{q}$ form.
Solution:
$4. \overline{7}$
Let $x = 4.7777....$
Multiply both sides by 10.
$10x = 10(4.7777....)$
$10x = 47.7777.....$
Therefore,
$10x-x = 47.7777.... - 4.7777.....$
$9x = 43$
$x = \frac{43}{9}$
Therefore,
$4. \overline{7}$ in $\frac{p}{q}$ form is $\frac{43}{9}$.
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