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# Which number is equal to $(\dfrac{{0.1}}{{0.01}} + \dfrac{{0.01}}{{0.1}})$?$A)10.1$$B)1.10$$C)1.01$$D)10.01$

Last updated date: 24th Jul 2024
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Hint: First we have to define what the terms we need to solve the problem are.
Since we need to know about the division and addition operator. A divisor is a number that will divide another number either completely (remainder zero) or with a remainder (real numbers)${\text{ }}\dfrac{{Dividend}}{{Divisor{\text{ }}}} = {\text{ }}Quotient$. And for the addition operator the things are very simple; Addition is the sum of two or more than two numbers, or values, or variables, and in addition if we sum the two or more numbers a new frame of the number will be found.

Complete step-by-step solution:
Since the given questions are in decimals and we will first convert into the whole numbers so that we can simply solve by using the division and addition operators;
Let us first convert; $\dfrac{{0.1}}{{0.01}} \times \dfrac{{100}}{{100}}$ (so the denominator will be a whole number and easy to divide)
Solving we get $\dfrac{{0.1}}{{0.01}} \times \dfrac{{100}}{{100}} = \dfrac{{10}}{1}$ and the answer is $10$ (by division we obtained this much simplification)
Now take that second term which is $\dfrac{{0.01}}{{0.1}} \times \dfrac{{10}}{{10}}$ and multiplied and divided by ten because the denominator needs to be one and hence solving, we get; $\dfrac{{0.01}}{{0.1}} \times \dfrac{{10}}{{10}} = \dfrac{{0.1}}{1} = 0.1$(by division algorithm)
Finally, we just need to add both the terms using the addition algorithm which is $(\dfrac{{0.1}}{{0.01}} + \dfrac{{0.01}}{{0.1}}) = 10 + 0.1 = 10.1$ and hence option $A)10.1$ is correct.
Since there isn’t any possibility of getting options like $B)1.10$, $C)1.01$, $D)10.01$
Because of the division algorithm and addition property; the first term gets ten and the second term gets zero point one; if we use it correctly, we only get option A

Note: We can also able to solve this problem (without converting) by just divide the terms inside like $\dfrac{{0.1}}{{0.01}} = 10$and $\dfrac{{0.01}}{{0.1}} = 0.1$ hence finally add them using the addition property and thus we get the same result.