Express the following in the form p/q, where p and q are integers and q ≠ 0
0.6 (6 is in bar) bar .6
Solution:
To express the decimal number 0.6 with the recurring bar over the 6 as a fraction in the form p/q, we can use the method of algebraic manipulation.

Let's denote the repeating decimal as x:

x = 0.666...

Now, we multiply both sides of the equation by 10 to shift the decimal point:

10x = 6.666...

Next, we subtract the original equation from the multiplied equation to eliminate the repeating decimal:

10x - x = 6.666... - 0.666...

Simplifying the equation:

9x = 6

Dividing both sides by 9:

x = 6/9

Since 6 and 9 have a common factor of 3, we can simplify the fraction:

x = 2/3

Therefore, the decimal number 0.6 (with the recurring bar over the 6) can be expressed as the fraction 2/3.

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