Question

PLZ HELP!!!!!!! WILL MARK BRAINIEST!!!!!!
express 0.1254 in p/q form

the bar is over 5 and 4

Answer 1

$\dfrac{p}{q}=0.12\overline{54}\\\\\\\dfrac{p}{q}=0.1254545454\ldots\qquad|\cdot100\\\\\\100\cdot\dfrac{p}{q}=12.54545454\ldots\\\\\\100\cdot\dfrac{p}{q}=12+0.54545454\ldots$

Now let:

$x=0.54545454\ldots\qquad|\cdot100\\\\100x=54.54545454\ldots\\\\100x=54+0.54545454\ldots\\\\100x=54+x\\\\99x=54\qquad|:99\\\\\\\boxed{x=\dfrac{54}{99}}$

So:

$100\cdot\dfrac{p}{q}=12+0.54545454\ldots\\\\\\100\cdot\dfrac{p}{q}=12+x\\\\\\100\cdot\dfrac{p}{q}=12+\dfrac{54}{99}\\\\\\100\cdot\dfrac{p}{q}=12\cdot\dfrac{99}{99}+\dfrac{54}{99}\\\\\\100\cdot\dfrac{p}{q}=\dfrac{1188}{99}+\dfrac{54}{99}\\\\\\100\cdot\dfrac{p}{q}=\dfrac{1242}{99}\\\\\\100\cdot\dfrac{p}{q}=\dfrac{138}{11}\qquad\Big|:100\\\\\\\dfrac{p}{q}=\dfrac{138}{11\cdot100}\\\\\\\dfrac{p}{q}=\dfrac{138}{1100}\\\\\\\boxed{\dfrac{p}{q}=\dfrac{69}{550}}$