Question

How to write 108 million in scientific notation?

Answer 1

Hint: We will first write 1 million in scientific terms and then multiply both sides by 108 and then later write 108 as 1.08 multiplied by 100 to further write in final scientific notation.

Complete step-by-step answer:
We are given that we are required to write 108 million in scientific notation.
We know that 1 million in Indian currency means 10 lakhs.
We know that 1 lakh is written as 1,00,000.
Multiplying the equation by 10, we will get:-
10 Lakhs is written as 10 times 1,00,000 that is equal to 10,00,000.
Now, we have concluded that 1 million is written as 10,00,000.
We can write it as: 1 million = ${10^6}$.
Now, multiplying both side by 108, we will get:-
$ \Rightarrow $108 million = $108 \times {10^6}$. …………….(1)
We can write 108 as: \[108 = 1.08 \times 100\]
Rewriting this, we will get: \[108 = 1.08 \times {10^2}\]
Putting this in equation number 1, we will get:-
$ \Rightarrow $108 million = $1.08 \times {10^2} \times {10^6}$
Now, we will use the fact that ${a^x}.{a^y} = {a^{x + y}}$
$ \Rightarrow $108 million = $1.08 \times {10^{2 + 6}}$
Simplifying the calculations in the power, we will then obtain the following:-
$ \Rightarrow $108 million = $1.08 \times {10^8}$

Hence, the required scientific notation of 108 million is $1.08 \times {10^8}$.

Note:
We use this kind of representation, where we raise a number to some power is a simple representation, which makes a number to be read easily for example if you need to write 10000000000, that is difficult to read, you will have to count the zeros in it and then see what number this forms but if you write it in the form ${10^{10}}$, we get an easier picture of the number and we instantly can read it without any issue.
Whenever you are given any number raised to any power, for example: say if a is raised to the power of b, that represents that you have to multiply the number as many times has the power. If we talk about the example, we have to multiply the number a for b times to get the required answer.