Question

How to write 108 million in scientific notation?

Answer 1

Hint: Find out if the number is multiple of 10. If the number is multiple of 10 the exponential part is written in scientific notation to the power of 10. The numerical part is obtained with only one digit of the number before the decimal as per the scientific notation rules.

Complete step by step solution:
In our calculations, we encounter numbers with a lot of leading zeros that increases the complexity while performing operations. Scientific notation helps in making very large or very small numbers simpler so that they can be easily read and understood.
Scientific notation of a number has two parts:
1). Numerical part consisting of a digit followed by its coefficient
2). Exponential part indicating number to the power of 10.
A million is followed by 6 zeroes. As per our question, 108 million is represented in numerical form as 108,000,000.
The n zeroes at the end of any number in scientific notation are represented as ${{10}^{n}}$ . Similarly, 108 million can be written as $108\times {{10}^{6}}$
The numerical part in Scientific notation should only have one digit before the decimal point. We must divide the number by ${{10}^{n}}$ to shift the decimal point to the left n times.
In our case, we must shift the decimal point to the left by only 2 places.
Dividing 108 by ${{10}^{2}}$ we get 1.08
$\Rightarrow 108=1.08\times {{10}^{2}}$
Replacing the value of 108 in the primary equation, we get scientific notation of the number as,
$\Rightarrow 1.08\times {{10}^{2}}\times {{10}^{6}}$
According to the law of exponents, when the same bases are to be multiplied their corresponding exponents are added. The formula is given by, ${{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$
$\Rightarrow 1.08\times {{10}^{2+6}}$
$\Rightarrow 1.08\times {{10}^{8}}$
Hence, the scientific notation of 108 million is $1.08\times {{10}^{8}}$

Note: Scientific notation is the way of expressing large numbers in decimal form. The n zeroes at the end of any number in scientific notation are represented to the power of 10 as $\left( {{10}^{n}} \right)$ . We must divide the number by ${{10}^{n}}$ to move the decimal point to the left n times.