Question

How do you write \[2,360,000\] in scientific notation?

Answer 1

Hint: According to the given question, we are trying to convert the given number where the form will range between \[1\] and \[10\]. To convert that, we will try to shift the decimal point or the decimal dot in a form where the resulting number will be greater than 1 but that number will also be less than 10.

Complete step by step solution:
The formula is \[m\times {{10}^{n}}\]
Let us solve the given problem,
The scientific form or the standard form is written in a specific pattern or in a specific form. The form is
\[m\times {{10}^{n}}\]
In this formula \[m\]is the number which will range between \[1\] and \[10\],\[n\] is the exponent that can be either a negative or positive number.
After this we will convert the given number into scientific notation. To do this, we will shift the decimal point six times to the left. In simple terms, we can say that we make the decimal point jump over the left side six times.
Now, we got out \[m\] to be \[2.36\]as a result. If we notice that \[m\]is now in the range between \[1\] and \[10\]. The number now is greater than 1 and less than 10.
We had shifted the decimal point sixth place over left, so the exponent which is denoted by the symbol \[n\] is \[6\]. Here, the \[n\]will be positive, because it is shifting to the left side. So,\[n=6\].
In numerical form,
\[{{10}^{6}}=1000000\]
\[\dfrac{2,360,000}{1000000}=2.36\]
\[\Rightarrow 2.36\times 1000000=2360000\]
Therefore, the result is:

\[\therefore 2360000\]is \[2.36\times {{10}^{6}}\] in scientific notation.

Note:
One important thing to remember is to always shift the decimal points correctly and to count the number of zeros properly to avoid any kind of mistake. The value of \[n\] cannot be equal to 10 or -10.
We can ignore the zeros after decimal points and in case we have non-zero digits after 0 after decimal, we can’t ignore these zeroes.