Question

Convert 0. 003522222... In the form of p/q

Answer 1

Here the decimal number is recurring
steps followed are,

Step I: Let us assume ‘x’ to be the repeating decimal number we are trying to convert into rational number.

Step II: Carefully examine the repeating decimal to find the repeating digits.

Step III: Place the repeating digits to the left of decimal point.

Step IV: After step 3 place the repeating digits to the right of decimal point.

Let x=0.00352222

Here 2 is the repeating digit
We need to take the repeating digits to left side,
Multiplying by 100000
100000x=352.222
Now taking repeating digit to the right side
10000x=35.2222

100000x-10000x=352.2222-35.2222
90000x=317
x=317/90000