Question

How do you simplify and make the decimal \[0.225\] into a fraction?

Answer 1

Hint: In the given question, we are given a decimal number and we have to convert the given decimal number into a fraction and then we have to simplify it. We will first write the decimal number without the decimal point as the numerator and then we will annex 1 following zeroes proportional to number of decimal places in the given decimal number, that is, we will have \[\dfrac{225}{1000}\]. We will then reduce or simplify the obtained fraction in the simplest form possible. Hence, we will have the required answer.

Complete step-by-step solution:
According to the given question, we are given a decimal number, we are asked to convert it into a fraction and then we will be reducing it further.
A decimal number refers to the numbers that are intermediate to the integers and non-integers. And it can be said to be based on tens units. So, in a decimal number, past the decimal point we have the tenths, hundredths and so on.
The decimal number we have is,
\[0.225\]-----(1)
To write a fraction, we need to have a numerator and a denominator.
We will first write the given decimal number without the decimal point as the numerator of the fraction to be obtained.
Then, we will write the denominator annexed with 1 followed by number of zeroes proportional to the number of decimal places as seen in the given decimal number. We have,
\[= \dfrac{225}{1000}\]-----(2)
Now, in equation (2), we have the required fraction but we have to simplify it further. So, we will divide both the numerator and the denominator by 5, we will get,
\[= \dfrac{45}{200}\]----(3)
We can see that the equation (3) can be further reduced, so dividing the numerator and denominator by 5 in equation we get,
\[= \dfrac{9}{40}\]
Therefore, the simplest fractional form of the given decimal \[0.225\] is \[\dfrac{9}{40}\].

Note: The number of zeroes following the annexed 1 in equation (1) should be correctly written. In simple terms, the number of places the decimal point shifts is equal to the number of zeroes following the annexed 1 in equation (2). For example – If the decimal number is \[0.5\] then the decimal point is shifted one place towards the right so the fractional equivalent is \[\dfrac{5}{10}\]. And if the decimal is \[0.05\], the decimal is shifted two places towards the right, so the fractional equivalent is \[\dfrac{5}{100}\].