Question

How do you convert $ - 52,320,000$ in scientific notation?

Answer 1

Hint: In this question we are required to convert a small number to its scientific notation. Scientific notation is a way of representing numbers into two parts, one part contains the significant digits of the number and the other part contains a number to the power of $10$. Scientific notation is written in the form $a \times {10^b}$, where $a$ is the decimal number which is greater than or equal to $1$ and less than or equal to $10$ i.e. $1 \leqslant \left| a \right| \leqslant 10$. It can be read as “$a$ times $10$ to the power $b$”

Complete step by step solution:
We are given,
$ - 52,320,000$
To start converting, we need to place the decimal point in your number until there is only one non-zero digit to the left of the decimal, i.e the coefficient should lie between the given range, it will be known as a.
$ \Rightarrow - 5.2320000$
Now we’ll count the places we have moved the decimal that would be our b
$ \Rightarrow - 5.2320000 \times {10^7}$
Finally, we’ll remove all the zeros after the decimal
$ \Rightarrow - 5.232 \times {10^7}$

Note: Moving the decimal to the left the exponent of $10$ is positive, $b = $positive
Moving the decimal to the right the exponent of $10$ is negative, $b = $negative
If we do not move the decimal then the exponent of $10$ is $0$, $b = 0$.
There are few rules which need to be kept in mind while converting into scientific notation
The base of b is always zero.
The exponent should be a non-zero integer
The coefficient i.e. a should carry a positive or negative sign ahead of it.
The mantissa should carry the rest of the significant digits.