Express the following rational numbers in the form (p)/(q), p, q are integers, q!=0. (i) 6. bar(46) (ii) 0.1 bar(36) (iii) 3. bar(146) (iv) 5. bar(12)

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Convert to Fraction: Given the number 6. bar(46), let's denote it as x. x = 6.464646... To convert this into a fraction, we will use the following method: Let's multiply x by 100 to shift the decimal two places to the right. 100x = 646.464646... Now, subtract the original x from this new equation to get rid of the repeating decimals. 100x - x = 646.464646... - 6.464646... 99x = 640 Now, we can solve for x by dividing both sides by 99. x = 640 / 99Check for Simplification: Now let's check for any simplification. 640 and 99 have no common factors other than 1, so the fraction is already in its simplest form.Convert to Fraction: For the number 0.1 bar(36), let's denote it as y. y = 0.1363636... To convert this into a fraction, we will use the following method: First, multiply y by 10 to shift the non-repeating decimal to the left of the decimal point. 10y = 1.363636... Now, multiply y by 1000 to shift the repeating decimals three places to the right. 1000y = 136.363636... Subtract 10y from 1000y to get rid of the repeating decimals. 1000y - 10y = 136.363636... - 1.363636... 990y = 135 Now, we can solve for y by dividing both sides by 990. y = 135 / 990Simplify Fraction: Let's simplify the fraction 135/990. Both the numerator and the denominator are divisible by 135. 135 / 135 = 1 990 / 135 = 7.4 However, the denominator should be an integer, so we made a mistake in our simplification. Let's correct it. Both the numerator and the denominator are divisible by 45. 135 / 45 = 3 990 / 45 = 22 So, the simplified fraction is 3/22.

Express the following rational numbers in the form $\frac{p}{q}$ , $p$ , $q$ are integers, $q\neq 0$ . $\newline$ (i) $6.\overline{46}$ $\newline$ (ii) $0.1\overline{36}$ $\newline$ (iii) $3.\overline{146}$ $\newline$ (iv) $-5.\overline{12}$

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Express the following rational numbers in the form pq\frac{p}{q}qp​, ppp, qqq are integers, q≠0q\neq 0q=0. \newline(i) 6.46‾6.\overline{46}6.46\newline (ii) 0.136‾0.1\overline{36}0.136 \newline(iii) 3.146‾3.\overline{146}3.146\newline (iv) −5.12‾-5.\overline{12}−5.12

Express the following rational numbers in the form $\frac{p}{q}$ , $p$ , $q$ are integers, $q\neq 0$ . $\newline$ (i) $6.\overline{46}$ $\newline$ (ii) $0.1\overline{36}$ $\newline$ (iii) $3.\overline{146}$ $\newline$ (iv) $-5.\overline{12}$