Question

Write $0.0005$ as a fraction.

Answer 1

Hint: To convert $0.0005$ as fraction let’s first convert it into scientific form and then further simplify it. Scientific notation 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 using the above information we can solve the given question.

Complete step-by-step solution:
Given
$0.0005............................\left( i \right)$
So to represent $0.0005$ as a fraction let’s first represent it in scientific form and then further simplify it.
So by the basic definition of scientific notation the numbers are represented in the form $p \times {10^n}$where \[1 \leqslant p \prec 10\] and $n$ is an integer.
Such that we have to find$p\;{\text{and}}\;n$ for the number $0.0005$
Now in order to find $p$ we have to move the position of decimal such that there is only a single digit before it.
So we get:
$ \Rightarrow 0.0005 = 00005.0\;\;................\left( i \right)$
So we can write$p = 5$
Now in order to find $n$ we have to determine the position of decimal which has been moved:
So here since it has been moved to the right side by $4$ positions, we can write:
$n = {10^{ - 4}}........................\left( {ii} \right)$
The sign would be negative since it has been shifted to the right side.
So from (i) and (ii) we can write:
$
   \Rightarrow p \times {10^n} = 5 \times {10^{ - 4}} \\
   \Rightarrow 0.0005 = 5 \times {10^{ - 4}}..........\left( {iii} \right) \\
 $
Now let’s further simplify (iii):
We know that: ${x^{ - n}} = \dfrac{1}{{{x^n}}}$
$
   \Rightarrow {x^{ - n}} = \dfrac{1}{{{x^n}}} \\
   \Rightarrow {10^{ - 4}} = \dfrac{1}{{{{10}^4}}}..........................\left( {iv} \right) \\
 $
Now let’s substitute (iv) in (iii) we get:
$
 \Rightarrow 5 \times {10^{ - 4}} = 5 \times \dfrac{1}{{{{10}^4}}} \\
\Rightarrow 5 \times {10^{ - 4}} = \dfrac{5}{{10000}} \\
\Rightarrow 5 \times {10^{ - 4}} = \dfrac{5}{{5 \times 2000}} \\
\Rightarrow 5 \times {10^{ - 4}} = \dfrac{1}{{2000}}........................\left( v \right) \\
 $

Therefore $0.0005$ as a fraction can be represented as: $\dfrac{1}{{2000}}$

Note: To convert the general format numbers to scientific notation form the standard rules have to be followed. While representing a number in fraction it’s always best to represent in the simplified form. Also the above prescribed method is one of the most efficient one to represent a decimal in fraction.