Question

How do you write $15.5 \times {10^4}$ in scientific notation?

Answer 1

Hint: In this question we are required to convert a number to its correct 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,
$15.5 \times {10^4}$
To convert it into scientific form, we need to be sure that there is only one number to the left of the decimal point. Since the above expression has two significant digits, we'll have to shift the decimal further to left and increase the exponent simultaneously.
$ \Rightarrow 1.55 \times {10^5}$
This is the required answer.

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 $0$, $b = 0$. $ \Rightarrow - 5.2320000 \times {10^7}$
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.