Question

How do you simplify ${10^2} \times 0.23$?

Answer 1

Hint: We will first of all simplify the term 10 raised to the power of 2 by multiplying 10 two times and then we will just multiply it by 0.23 and move the decimal as required.

Complete step-by-step solution:
We are given that we are required to simplify the given expression which is ${10^2} \times 0.23$.
We see that, here two terms are being multiplied, one is ${10^2}$ and the other term is 0.23.
We know that square of any number means we need to multiply that number two times.
Therefore, 10 raised to the power of 2 means that we have to calculate 10 multiplied by 10 which can also be written as: ${10^2} = 10 \times 10$.
Since we know that 10 multiplied by 10 always gives 100.
Therefore, we will have the following expression with us:-
$ \Rightarrow {10^2} = 10 \times 10 = 100$
Now, we just need to multiply 100 by 0.23
Since, we know that we have to move the decimal as many numbers of zero we have.
Here, in 100 we have two zeroes, therefore we will have to move the decimal two places later.
Now, it is before 2 in 0.23, moving it one place, we will get 2.3 instead of 0.23, but we have to move it one more place. So, moving one place ahead more, we will get 23 instead of 0.23.

Hence, we have ${10^2} \times 0.23 = 23$.

Note: The students must note that if we have 10, 100 or 1000 and so on in the division part, then we move the decimal in the opposite position as we did in the above solution.
For example:- If we would have been given $\dfrac{1}{{{{10}^2}}} \times 23$, we would have to write it as: $\dfrac{1}{{100}} \times 23$, then we will have to move decimal from 23.
Since 23 can be written as 23.0, we will have to move it two place earlier, thus we have the required answer as 0.23