Question

Write $ 4.5 \times {10^3} $ in standard form.

Answer 1

Hint: Standard form of a number is the representation of numbers in such a way that very large numbers can be read easily without any discrepancy. Also in scientific notation the numbers are represented in the form $ p \times {10^n} $ where $ p $ should be between 1 and 10 i.e. \[1 \leqslant p \prec 10\]and $ n $ is an integer.
So in this question, we have been given the number in scientific notation which we have to write in a standard form such that all the processes which are done to represent a number in scientific notation have to be in reverse. In simple words, we just need to multiply it with the power i.e. $ {10^n} $ .

Complete step by step answer:
Given
 $ 4.5 \times {10^3}......................\left( i \right) $
We need to convert (i) from the form $ p \times {10^n} $ to standard form.
Since the power is positive here we have to move the decimal digit to the right by three points.
 $
   \Rightarrow 4.5 \times {10^3} = 4500.0 \\
   \Rightarrow 4.5 \times 10 = 4500...............\left( {ii} \right) \\
  $
So (ii) represents the standard form and is the final answer.
Therefore the standard form of $ 4.5 \times {10^3} $ is $ 4500 $ .

Note:
To convert the general format numbers to scientific notation form certain rules have to be followed as given below:
1. The position of the decimal point should be such that there is only a single digit before it.
2. While moving the decimal points one should take care of the position which has been moved since it determines the power of 10.
3. Also the direction to which the decimal point has been moved is to be noted, if it has been moved to the left then the power is positive and if it’s moved to the right then the power is negative.