Question

How do you write 41,000,000 in scientific notation?

Answer 1

Hint: We will first write all the zeroes in the form of raising power to 10 and then see what we are left with and then introduce a decimal so that we get 1 digit before decimal.

Complete step-by-step answer:
We have the number 41,000,000 with us which needs to be written in scientific notation. Now, we can see that it has clearly 6 zeroes at the end after 41 in it.
We can write 1,000,000 as ${10^6}$.
Now, if we multiply both sides by 41, we will obtain:-
41,000,000 can be written as $41 \times {10^6}$.
Now, we know that in scientific notation, we need only 1 digit before the decimal but here we have 2 which are 4 and 1.
Now we will write 41 as 4.1 multiplied by 10.
$ \Rightarrow $41,000,000 can be written as $4.1 \times 10 \times {10^6}$.
$ \Rightarrow $41,000,000 can be written as $4.1 \times {10^7}$.

Hence, the answer is $4.1 \times {10^7}$.

Note:
The students must note that in the last few steps we used the fact that: ${x^a} \times {x^b} = {x^{a + b}}$.
Therefore the powers of 10 which were 6 and 1 got added and thus we got 7 on 10.
The students must know the following facts about scientific notation:-
Scientific notation is a method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10.
It helps us to get an idea of the number without writing all the zeroes and in an easier form.
For example writing 10 raised to power 20 will be 100000000000000000000 and ${10^{20}}$.
We can clearly observe that we will have to count zeros in 100000000000000000000 and get the idea what it stands for whereas reading ${10^{20}}$ gives a clear idea of it.
Therefore, we have applications of scientific notations as well.