Question

Express 1.235bar in the form p/q, where p and q are integers and q≠0​

Answer 1

Answer:

1223/990 is the required form.

Step by step explanation:

Express this number in the form p/q where p and q are integers and q ≠ 0

• 1.2353535...

Let a = 1.23535.. ...( 1 )

10a = 12.3535.. ...( 2 )

100a = 123.53535.. ...( 3 )

1000a = 1235.3535.. ...( 4 )

Subtracting (2) from (4)

⇛ 1000a - 10a = 1235.3535.. - 12.3535..

⇛ 990a = 1223

⇛ a = 1223/990

Value of 1.23535.. is 1223/990.

━━━━━━━━━━━━━━━━━━━━━━

We were actually asked to convert the given number into a rational number, A rational number is of the form p/q, where both p and q are integers and q≠0. In other words, a rational number is a number which can be expressed as a ratio of two integers.

examples of rational numbers: 4, 4/5, 7/9 etc. Note that 3/0 or 1/0 is not a Rational number as division by zero is not defined.