Question

How do you write 4,000,000 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 solution:
Now considering from the question we have the number $4,000,000$ .
We have to follow the steps below to see how $4,000,000$ 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: $4,000,000$
New number: $4.000000$
Step $2$: Now to find $b$, count how many places to the right of the decimal
New number: $4\text{ }\text{. 0 0 0 0 0 0}$
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 $a\times {{10}^{b}}$
$a=4$ (Please notice any zeroes on the end have been removed)
$b=6$
Now, the whole thing: $4\times {{10}^{6}}$
Step $4$: now, we have to check our work
 $\begin{align}
  & 4\times {{10}^{6}}=4\times 1,000,000 \\
 & \Rightarrow 4,000,000 \\
\end{align}$
Hence, verified.

Note: While answering questions of this type we should be sure with the calculations. For answering this question we have to write the scientific notation which helps in writing large numbers with ease which is very helpful for scientists in today’s generation. Generally as we decimal number system we express the scientific notation as the exponents of $10$.