Question

A micron is \[1\times {{10}^{-6}}\] metre. How do you write that number and unit in standard form?

Answer 1

Hint: Solving these types of problems are very easy once we know the underlying concepts and formulae in depth and detail. In this particular given problem, we need to have an idea of the topic units and measurements and also its applications to some extent. The conversion from one type to another becomes very handy in these kinds of problems. We first of all need to express the given statement from micron to metres in terms of a fraction, and after that we need to do a unit change and express the microns to millimetres for our convenience and for the simplicity of the solution of the problem.

Complete step-by-step solution:
Now we start off with the solution to our given problem by writing the given relation in terms of fraction, we thus write it as,
\[1\] micron = \[\dfrac{1}{1000000}\] metre
Now, from the relation of length in standard form we know that,
\[1\] millimetre = \[\dfrac{1}{1000}\] metre
Now, converting the micron in terms of millimetre, we get,
\[1\] micron = \[\dfrac{1}{1000}\] millimetre
The micron unit of length is actually very small and is generally denoted by \[\mu \] . Therefore, we can write,
\[1\mu \] = \[\dfrac{1}{1000}\] mm
Thus, this is our answer to the problem.

Note: For problems like these we need to have a fair idea of units and measurement and the conversion from one unit to another. We must be very careful while we are applying these transformations as these are the areas that are most prone to committing mistakes. The conversion from one system to another must be very well defined, or else we might not be able to use it.