Question

How do you express 418,000,000 in a scientific notation?

Answer 1

Hint: In the given question, we need to convert decimal notation to scientific notation. Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form. There is a specific way to represent the scientific notation. It is represented as:
$\Rightarrow a\times {{10}^{b}};1\le a<10$

Complete step by step answer:
Now, let’s discuss the question.
As we know that scientific notation is a form of presenting very large numbers or very small numbers in a simpler form. It helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit or decimal numbers and 10 raised to the power of the respective exponent. You should know that the exponent is positive if the number is very large and it is negative if the number is very small.
There is a systematic way of representing the scientific notation. It is represented as:
$\Rightarrow a\times {{10}^{b}};1\le a<10$
Where ‘a’ can be any number in the range of 1 to 10 including 1 but excluding 10. The reason for this is that it is used in the formation of exponent. Here, b is the power.
There are 2 rules for writing the scientific notation. They are:
First is, if a number is multiplied by 10, then the decimal point will move to the left and the power of 10 will be positive. For example: 6000 = $6\times {{10}^{3}}$ is in scientific notation.
Second is, if the number is smaller than 1, the decimal point will shift to the right and the power of 10 will become negative. For example: 0.006 = 6 × 0.001 = $6\times {{10}^{-3}}$ is in scientific notation.
In the given question, 418,000,000 is in decimal notation.
We have to follow rule one. The decimal will move left and the power will become positive.
$\Rightarrow $418,000,000 $\Leftrightarrow 4.18\times {{10}^{8}}$
8 represents that we have to move the decimal 8 times left from the right most position.

Note:
Apart from zero, if there are more than one digits then we will show with a decimal point. We will not show it like this: 418,000,000 $\Leftrightarrow 4\times {{10}^{8}}$. Because if we see only $4\times {{10}^{8}}$, then it means 400,000,000 but actually this was not that number. So it gives the wrong answer.