Question

Write the following decimal number as fraction in lowest form $0.225$ .

Answer 1

Hint: A fraction has two parts. The upper part is called numerator and the lower part is called denominator. Let $f$ be a fraction. So, $f$$=\dfrac{a}{b}$ , so, here, $a$ is a numerator and $b$ is a denominator of fraction$f$.

Complete step-by-step answer:
Now, decimal is also called base – ten positional numbers. For example $45.6$, so, here,$4$ is at tens place, $5$ is at one place and after that there is a dot ( it is called decimal point ) after decimal point $6$is at tenths place and so on. So, here, to write $45.6$ in fractional form we write it as $45.6=\dfrac{456}{10}$ .
After a point there is one number, so write one zero after $1$ in denominator.

Now, the question is to write $0.225$ in lowest form. For that we first write $0.225$ in fractional form.
So, as in $0.225$ we can see there are three numbers after the decimal point in $0.225$.So, hence, we write three zeroes after $1$ denominator.
So, $0.225$$=\dfrac{225}{1000}$
Now, to write in lowest form of fraction one must convert the fraction into such that the numerator and denominator have no common factor in between them other than $1$. Then, it is said to be in lowest form or simplest form or else in other ways we can also say that if HCF (highest common factor) of numerator and denominator is$1$ then it is in lowest form or simplest form. For this we cancel out all the common factors other than $1$ (which cannot be cancelled out). So, we factorise $225$ and $1000$, to proceed;
$225=5\times 5\times 3\times 3$
$1000=2\times 2\times 2\times 5\times 5\times 5$
Now, $0.225$$=\dfrac{225}{1000}$ $=\dfrac{5\times 5\times 3\times 3}{2\times 2\times 2\times 5\times 5\times 5}$
So, we cancel out all common factors in the given fraction which is$25$
So, we get; $\dfrac{225}{1000}$ $=$ $\dfrac{9}{40}$
Clearly, $9$ and $40$ have no common factor other than one. Means it's HCF (highest common factor) is $1$.
So, it is by definition in lowest form. So, the lowest form of $0.225$ is $\dfrac{9}{40}$ respectively.

Note: In the process of converting one must find all the common factors and cancel it out. For that just factorise the numerator and denominator.
All integers are always in lowest form because their denominator is one ,so the HCF between numerator and denominator is always one. So, always in lowest form.