Question

How is $0.0120$ written in scientific notation?
A. $120\times {{10}^{-4}}$
B. $1.2\times {{10}^{-2}}$
C. $12\times {{10}^{-3}}$
D. $12.0\times {{10}^{-3}}$

Answer 1

Hint: Think about how a number can be expressed in an easy way by changing the order of magnitude of any number. The easiest number to read would be a ‘single-digit’ number and just a glance at the order of magnitude would give us an idea about its scale.

Complete step by step answer:
All numbers that are written in scientific notation have easy readability and are always effective in giving us an idea about the scale at which the comparison of the values should occur.
The scientific notation of any number consists of two parts, a decimal number whose absolute value must lie within strict set points and an order of magnitude part which tells you the power in powers of 10.
The rule for the first part of the notation is that the absolute value of the decimal should lie between 0 and 10. If ‘a’ is the decimal part, this is mathematically denoted as:
\[0<\left| a \right|<10\]
In the second part, the power of 0 should be adjusted such that the scientific notation becomes equal to the original number. Both these parts are written as a product for the complete scientific notation.
For the scientific notation of the number 0.0120 we will follow the steps:
- Write number as a; 1.2
- Since we moved the decimal forward by two place values, we should adjust the power of 10 so that it indicates that the decimal should be moved 2 place values back to obtain the original number.
- multiply the decimal by ${{10}^{-2}}$
Hence, the correct answer is ‘B. $1.2\times {{10}^{-2}}$’.

Note: It may seem easier to just consider numbers between 0 and 100, since they are easily readable too. But this will create problems in the interpretation of the order of magnitude since the decimal spans over 2 orders (0-10, 10-100) rather than just 1 (1-10).