The fractional part of decimal number system can be convertedd into binary by multiplying the decima fractional with '2'.

Step 1: Begin with the decimal fraction and multiply by '2'. The whole number part of the result is the first binary digit to the right of the point.

$0.42\times 2=0.84\rightarrow$ the first binary digit to the right of the point is "0".

Step 2:Now, consider the decimal fraction of the previous result and multiply by "2". The whole number part of this new result is the second binary digit to the right of the point.

$0.84\times 2=1.68\rightarrow$ the second binary digit to the right of the point is "1".

Step 3: Disregarding the whole number of the previous result, multiply by 2 once again. The whole number part of this new result is the third binary digit to the right of the point.

$0.68\times 2=1.36\rightarrow$ the third binary digit to the right of the point is "1".

Step 4: Disregarding the whole number of the previous result and multiply by "2" once again. The whole number part is the fourth binary digit to the right of the point.

$0.36\times 2=0.72\rightarrow$ the fourth binary digit to the right of the point is "0".

Here, the decimal fraction may not become zero in such conversion. So we need to represent till 4 to 5 digits of the right of the point,

$(0.42)_{10}=(0.0110....)_2$.