Question

Express in the form of p/q
12.53bar +0.23bar

Answer 1

Step-by-step explanation:

Given:

$12. \overline{53} + 0.\overline{23}$

To find: Express in the form of p/q

Solution:

Let

$x = 12. \overline{53} + 0.\overline{23}$

Step 1: Remove bar

$x = 12.535353... + 0.232323...$

Step 2: Express x in terms of two constant

$x = x_1 + x_2 \\ \\ x_1 = 12.535353... \\ \\ x_2 = 0.232323...$

Step 3: Write x1 in terms of p/q

$x_1 = 12.535353... \\ \\ 100x_1 = 1253.535353... \\ \\ subtract \: both \\ \\ 99x_1 = 1241 \\ \\ x_1 = \frac{1241}{99}$

Step 4: Write x2 in terms of p/q

$x_2 = 0.232323... \\ \\ 100x_2 = 23.232323... \\ \\ subtract \\ \\ 99x_2 = 23 \\ \\ x_2 = \frac{23}{99}$

Step 4: Find x by adding both x1 and x2

$x = \frac{1241}{99} + \frac{23}{99} \\ \\ x = \frac{1241 + 23}{99} \\ \\ x = \frac{1264}{99}$

Final Answer:

$\bold{12. \overline{53} + 0.\overline{23} = \frac{1264}{99}}$

This way the given expression can be written in terms of p/q form.

Hope it helps you.

To learn more on brainly:

write 357.417417... in p/q form

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Answer 2

$\underline{\textbf{Given:}}$

$\mathsf{12.\overline{53}+0.\overline{23}}$

$\underline{\textbf{To find:}}$

$\mathsf{\dfrac{p}{q}\;form\;of\;12.\overline{53}+0.\overline{23}}$

$\underline{\textbf{Solution:}}$

$\mathsf{Let\;x=12.\overline{53}+0.\overline{23}}$

$\mathsf{x=12.535353\;.\;.\;.\;.+0.232323\;.\;.\;.\;.}$

$\implies\mathsf{x=12.767676\;.\;.\;.\;.}$----------(1)

$\mathsf{100\,x=1276.767676\;.\;.\;.\;.}$----------(2)

$\mathsf{(2)-(1)\;\implies}$

$\mathsf{100x-x=1276-12}$

$\mathsf{99\,x=1264}$

$\implies\mathsf{x=\dfrac{1264}{99}}$

$\therefore\boxed{\mathsf{12.\overline{53}+0.\overline{23}=\dfrac{1264}{99}}}$

$\underline{\textbf{Find more:}}$

Express 0.432323 in the form p/q, where p and q are integers and q not equal to 0

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