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Express 3.565656..... in $\frac{p}{q}$ form.
Given :
The given number is 3.5656...
To do :
We have to express the given number in $\frac{p}{q}$ form.
Solution :
Let the given number be x.
$x=3.5656....$
Multiply both sides by 10.
$10x=10(3.5656....)$
$10x=35.65656....$
Multiply both sides by 100.
$100(x)=100(3.5656....)$
$100x=356.5656.....$
Subtract x from 100x.
$100x-x=356.5656.... - 3.5656....$
$99x = 356-3$ (Since the digits after the decimals are same)
$99x=353$
$x=\frac{353}{99}$.
Therefore,
$3.5656...... = \frac{353}{99}$.
Therefore, 3.5656... can be expressed as $\frac{353}{99}$.Advertisements