Question

How do you express the number in scientific notation given the diameter of Neptune: \[49,600,000m\]?

Answer 1

Hint: In this question we are required to convert a large 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,
\[49,600,000m\]
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 4.9600000 $
Now we’ll count the places we have moved the decimal that would be our b
 $ \Rightarrow 4.9600000 \times {10^7} $
Finally, we’ll remove all the zeros after the decimal
\[ \Rightarrow 4.96 \times {10^7}\]
So, the correct answer is “\[ 4.96 \times {10^7}\]”.

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.