Question

How do you convert $ - 0.2$ to a fraction in simplest form?

Answer 1

Hint:Convert the decimal into fraction by following steps:
1. Write the decimal number as the numerator of the fraction.
2. In denominator write $10$
3. Find how many digits are there after the decimal in the given decimal number.
4. If there are \[n\] digits then, raise \[n\] to the power of $10$ in the denominator and remove the decimal. You will get the required fraction now to simplify it in order to find your answer.

Complete step by step solution:
In order to convert decimal numbers $ - 0.2$ into fraction, we need to follow some steps; there is no formula for converting decimal numbers into fraction directly.
We will write $ - 0.2$ as numerator of the fraction and $10$ in denominator, since $ - 0.2$ has only one digit after the decimal point so power of $10$ will be $1$
\[ - 0.2 = \dfrac{{ - 02}}{{{{10}^1}}} = \dfrac{{ - 2}}{{10}}\]
We got the fractional form $ = \dfrac{{ - 2}}{{10}}$
Now to simplify it, we will find the HCF (Highest Common Factor) between numerator and denominator and then divide both of them by HCF to get the simplest form.
$
- 2 = - 1 \times 2 \\
10 = 2 \times 5 \\
$
So we can see that HCF of $ - 2\;{\text{and}}\;10$ is $2$
Dividing both by $2$ we will get
$ = \dfrac{{ - 2 \div 2}}{{10 \div 2}} = \dfrac{{ - 1}}{5}$
$\therefore $ required fraction in simplest form is $ - 0.2 = \dfrac{{ - 1}}{5}$

Note: When counting the digits after decimal make sure that if $0$ is the last number then we don’t have to count it, if there exist digits after $0$ then count it but if $0$ is last then don’t count $0$ To convert recurring or repeating decimals into fraction, we have to go through different process, this the process is not for recurring decimals.