Question

10.03 bar 6

P/Q FORM
IN STEPS

Answer 1

HOW TO CONVERT THE REPEATING NON-TERMINATING DECIMAL INTO p/q FORM :-

1.write down the number in equals to a variable weighted Be X

1.write down the number in equals to a variable weighted Be X 2.multiply both the side that is the variable side and constant side in such a way that the digits under the bar get just to the left side of the decimal point .Mark it as first equation.

1.write down the number in equals to a variable weighted Be X 2.multiply both the side that is the variable side and constant side in such a way that the digits under the bar get just to the left side of the decimal point .Mark it as first equation.3.Follow Same step in bringing bar digits to the right side of the decimal point.Mark it as second equation.

1.write down the number in equals to a variable weighted Be X 2.multiply both the side that is the variable side and constant side in such a way that the digits under the bar get just to the left side of the decimal point .Mark it as first equation.3.Follow Same step in bringing bar digits to the right side of the decimal point.Mark it as second equation.4.Subtract eq. 01 from eq. 02.

1.write down the number in equals to a variable weighted Be X 2.multiply both the side that is the variable side and constant side in such a way that the digits under the bar get just to the left side of the decimal point .Mark it as first equation.3.Follow Same step in bringing bar digits to the right side of the decimal point.Mark it as second equation.4.Subtract eq. 01 from eq. 02.5.Obtain value of x in p/q form.

Solution of the question :-

$let \: 10.03 \overline{6}\: will \: be \: x \\ \\ \implies \: 100x = 1003. \overline{6} .....eq.01 \\ \\ \implies 1000x = 10036. \overline{6} ....eq.02\\ \\ subtracting \: eq.01 \: from \: eq.02 \\ \\ \implies 1000x - 100x = 10036. \overline{6} - 1003 \overline{6} \\ \\ \implies 900x = 9033 \\ \\ \implies \boxed{x = \frac{9033}{900} }$

Therefore, x is equals to both the repeating number and the p/q form.

Hence, the p/q form of the given decimal is obtained.