Question

How do you write 0.125 in scientific notation?

Answer 1

Hint: The scientific form of a number is a special notation in which the number can be written without changing its value. In scientific notation, the number is written with one digit to the left of the decimal and the remaining digits written to the right of the decimal. The number is then multiplied by a power of ten.

Complete step by step answer:
In this question, we are asked to write 0.125 in its scientific form. We know that the scientific form of a number is a special notation for a number of the form \[a\times {{10}^{n}}\], here a is a decimal number and n is an integer. The decimal number a has only 1 digit on the left side of the decimal point and the remaining digits on the right-hand side of the decimal point. It should be noted that the last digit on the right-hand side of the decimal should be non-zero.
Here the given number is 0.125, as we can see it has 3 digits after the decimal point. So, this number can also be written in the following way,
\[\begin{align}
  & \Rightarrow 0.125=125\times 0.001 \\
 & \Rightarrow 125\times {{10}^{-3}} \\
\end{align}\]
Multiplying and dividing the above number by 100, we get,
\[\begin{align}
  & \Rightarrow 125\times {{10}^{-3}}\times \dfrac{100}{100} \\
 & \Rightarrow \dfrac{125}{100}\times {{10}^{-3}}\times 100 \\
 & \Rightarrow 1.25\times {{10}^{-3}}\times {{10}^{2}} \\
 & \Rightarrow 1.25\times {{10}^{-1}} \\
\end{align}\]
As we can see that the above number satisfies the conditions for the scientific notation of a number. Hence, the scientific notation of 0.125 is \[1.25\times {{10}^{-1}}\].

Note:
Numbers that are larger than 1 can also be written in scientific notation, but the scientific notation for these numbers is of form \[a\times {{10}^{n}}\], here \[n\] is a positive integer. Similarly, negative numbers can also be written in scientific notation with a negative sign before it.