Question

How do you write $5+0.4$ as a decimal and a fraction?

Answer 1

Hint: To write the number as a decimal, we will add the digits before the decimal points using usual addition. Then we will add the digits after the decimal point in a way that the digits are written from the left and then add from the right. To write the number as a fraction, we will convert the decimal number to fraction and then add that to the whole number to get the sum in the form of a fraction.

Complete step by step answer:
Let us consider the given problem.
We are asked to write $5+0.4$ as a decimal and a fraction.
Let us first discuss how to write the number as a decimal.
To write this number as a sum what we need to do is to add the summands. Now, let us consider the first summand $5.$
It can be written as $5=5.0.$
Now the addition will take place as follows:
$\Rightarrow 5+0.4=5.0+0.4.$
We will add $5$ to $0,$ then put the decimal point. After that, we will add $0$ to $4$ to get
$\Rightarrow 5+0.4=5.4.$
Now, let us discuss how to write the given number as a fraction.
For that, let us convert the decimal number $0.4$ to fraction.
So, we will get $0.4=\dfrac{4}{10}.$
Now we will find the sum, $5+0.4=5+\dfrac{4}{10}=\dfrac{50+4}{10}=\dfrac{54}{10}.$
Let us cancel the common factor $2$ out to get $5+0.4=\dfrac{27}{5}.$
Hence the decimal form is $5.4$ and the fraction form is $\dfrac{27}{5}.$

Note:
We can convert it into the fraction form after the addition. So, after the addition we get the number in the decimal form, $5.4.$ Let us multiply and divide the number obtained with $10.$ We will get $5.4\times \dfrac{10}{10}.$ This will give us $\dfrac{54}{10}=\dfrac{27}{5}.$