Question

How do you convert \[3427\] into scientific notation?

Answer 1

Hint: These types of problems are pretty straight forward and are very easy to solve. Problems like these need a fair amount of understanding of the scientific notations and how they are done so as to achieve a consistency in the representation of numbers in mathematics. The general way of representing any number is to write the complete number how long it may be. But this type of representation is not accepted globally. So for this we need to write numbers in the form of scientific notation which can be understood by everyone. So the way of representing any number in the scientific form is to write it in the form,
\[x\times {{10}^{y}}\]
Here the number \[x\] varies from $1$ to $10$ . Mathematically we can write, \[1\le x<10\] . This way is acceptable to all and is thus generalised.

Complete step-by-step solution:
Now we start off with the solution to the given problem by writing it as,
 \[\begin{align}
  & 3427=3427\times 1 \\
 & \Rightarrow 3427=3427\times {{10}^{0}} \\
\end{align}\]
Now we know that we can write the any number in the decimal form as,
\[3427=3427.0\]
Thus replacing this in the previous equation we get,
\[\Rightarrow 3427=3427.0\times {{10}^{0}}\]
Now to make the number \[3427.0\] in between $1$ and $10$ we can simply move the decimal point towards the left 3 places and then multiply it with the required number of zeroes, i.e., $3$ . So we can write it as,
 \[\Rightarrow 3427=3.427\times {{10}^{0}}\times 1000\]
Now replacing the term $1000$ with the equivalent power of $10$ we get,
\[\Rightarrow 3427=3.427\times {{10}^{3}}\]
Thus, our answer to the problem is \[3.427\times {{10}^{3}}\] .

Note: These types of problems are very simple if we can understand why and how the scientific forms are required to represent different natural numbers. We must remember here that any number can be represented in the scientific form in this way and it is understandable to everyone. One of the main advantages of representing numbers this way is that the number ultimately becomes very easy to remember and we can hence focus on working on the problem rather than memorising large and complex numbers.