Question

Solve $301.01 - 0.101 = x + 198.01$.
A.$103.119$
B.$103.101$
C.$102.901$
D.$102.899$

Answer 1

Hint: Here in this question, we have to deal with addition and subtraction of decimal numbers. The most basic and easiest method of solving questions related to addition and subtraction of decimal numbers is by converting them into fractions. In order to solve this particular question, we have to first make sure that the decimal numbers are the same. For example- the decimal numbers in $301.01$ are two that is $.01$ whereas in $0.101$ there are three decimal numbers that is $.101$, similarly, in $198.01$ there are two decimal numbers that is $.01$. Then, we convert them in fractions and perform the addition or subtraction operations.

Complete step by step solution:
To keep the decimal numbers the same, we add zero at end. That zero does not affect the number at all.
So, we add zero at the end of $301.01$ so that it becomes $301.010$ whose value still remains the same. Similarly, we add zero to $198.01$ so that it becomes $198.010$ and its value also remains the same. We did this so that there are three decimal points or numbers behind every number.
Now we get,$301.010 - 0.101 = x + 198.010$
Next, we convert decimal numbers into fractions and we get,
$
   \Rightarrow \dfrac{{301010}}{{1000}} - \dfrac{{101}}{{1000}} = x + \dfrac{{198010}}{{1000}} \\
   \Rightarrow \dfrac{{301010 - 101}}{{1000}} = x + \dfrac{{198010}}{{1000}} \\
   \Rightarrow \dfrac{{300909}}{{1000}} = x + \dfrac{{198010}}{{1000}} \\
   \Rightarrow \dfrac{{300909}}{{1000}} - \dfrac{{198010}}{{1000}} = x \\
   \Rightarrow \dfrac{{300909 - 198010}}{{1000}} = x \\
   \Rightarrow \dfrac{{102899}}{{1000}} = x \\
   \Rightarrow 102.899 = x \\
 $
Hence, the value of $x$ is $102.899$

Therefore, the correct option is (D).

Note:
Here in the last step, we converted the fraction back to decimal numbers because all the options given to us were in decimal numbers. Therefore, we were expected to find the value of $x$ in decimal numbers only not in fractions. These types of questions are quite easy and just need simple calculations.