Given,
x=0.147777...
=> x×10= 0.147777...×10
=>10x=1.47777...
=>10x-x =1.47777...-0.14777...
=>9x=1.33
=>9x=133/100
=>x = 133/900

Converting 0.147(bar on 7) to p by q form:

To convert a recurring decimal to p by q form, we follow the steps mentioned below:

Step 1: Let x = 0.147(bar on 7)

Step 2: Multiply both sides by 10^2, as there are two digits after the decimal point.

x * 10^2 = 14.7777(bar on 7)

Step 3: Multiply both sides by 10, as we need to eliminate the recurring part.

10x = 147.7777(bar on 7)

Step 4: Subtract the equation obtained in step 2 from the equation obtained in step 3.

10x - x * 10^2 = 147.7777(bar on 7) - 14.7777(bar on 7)

Simplifying the equation, we get:

10x - x * 10^2 = 133

Step 5: Solve for x.

x = 133/900

Therefore, 0.147(bar on 7) = 133/900 in p by q form.

Explanation:

Recurring decimals can be converted to p by q form by following the above steps. The key is to multiply both sides by an appropriate power of 10 to eliminate the recurring part. Once we have obtained an equation without the recurring part, we can solve for the variable and express the number in p by q form. It is important to simplify the equation before solving for the variable to avoid errors in calculation.