Question

How do you write \[2,000,000\] in scientific notation?

Answer 1

Hint: The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease. Calculating scientific notation for a positive integer is simple, as it always follows this notation: \[a\times {{10}^{b}}\] where, \[a\] is a number or decimal number such that the absolute value of \[a\] is greater than or equal to one and less than ten \[1\le \left| a \right|<10\]

Complete step-by-step answer:
For answering this question we need to express the given number in scientific notation.
Calculating scientific notation for a positive integer is simple, as it always follows this notation: \[a\times {{10}^{b}}\] where, \[a\] is a number or decimal number such that the absolute value of \[a\] is greater than or equal to one and less than ten \[1\le \left| a \right|<10\].
We have to follow the steps below to see how \[2,000,000\]is written in scientific notation:
Step \[1\]: To find \[a\], take the number and move a decimal place to the right one position.
Original number: \[2,000,000\]
New number: \[2.000000\]
Step \[2\]: Now to find \[b\], count how many places to the right of the decimal.
New number: \[2.\text{ }0\text{ }0\text{ }0\ 0\text{ }0\text{ }0\text{ }\]
Decimal count: \[\text{ 1 2 3 4 5 6 }\]
There are six places to the right of the decimal place.
Step \[3\]: building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the scientific notation should be in the form of \[a\times {{10}^{b}}\]
Here, \[\text{a=2}\] (please notice any zeroes on the end have been removed)
\[\text{b=6}\]
Now, the whole thing: \[2\times {{10}^{6}}\]
Step \[4\]: now, we have to check our work
\[2\times {{10}^{6}}=2,000,000\]
Hence, verified.

Note: We should be well aware of the standard notation and scientific notation and the difference between them. We should know the process of how to convert the standard notation into scientific notation. We should be very careful while converting into the scientific notation. We should not make any mistakes especially while counting the decimal count. Also we have to verify in the end whether they are correct or not. Similarly we can express $2,000,000$ in terms of the power of $e$ as ${{e}^{14.5}}$ .