Question

How do you divide rational numbers in decimal form?

Answer 1

Hint: In order to divide two numbers which are in decimal form, we have to first convert them into the whole numbers by multiplying and dividing with the number $10$ raised to power number of digits after the decimal point. Now simply divide the whole numbers to get your required result.

Complete step by step answer:
Let's suppose we have two decimal numbers \[a\] and $b$. According to our question we have to divide these two numbers i.e. $\dfrac{a}{b}$.So in order to do so we have to follow some steps which are stated below.
Step 1: Since we gave two numbers in the decimal, so it’s very difficult to divide them. First, we have to convert both the decimal numbers into whole numbers. To convert the numbers into whole we have to multiply it with the number 10 raised to power the number of digits after the decimal point. But, in order to maintain balance, we have to multiply and divide, we can’t simply multiply or divide with any number.
Step 2: Simplify the fraction
Step 3: Now both numerator and denominator are converted into whole numbers, so we can easily divide them to obtain the quotient.
Let's suppose an example , we have $10.4$ and $2.6$ and we have to divide them. We can write $\dfrac{{10.4}}{{2.6}}$ as we can in both numerator and denominator we have one digit after the decimal point, so multiplying and dividing in the numerator as well as in denominator with the number $10$,we get
$
\dfrac{{10.4}}{{2.6}}= \dfrac{{10.4 \times \dfrac{{10}}{{10}}}}{{2.6 \times \dfrac{{10}}{{10}}}} \\
\Rightarrow\dfrac{{10.4}}{{2.6}}= \dfrac{{104}}{{26}} \\ $
We have now converted both the numbers into whole numbers , now simply dividing them.
As we know $26 \times 4 = 104$
$
\dfrac{{10.4}}{{2.6}}= \dfrac{{104}}{{26}} \\
\therefore\dfrac{{10.4}}{{2.6}}= 4 \\ $
Therefore, our required answer is $4$.

Note:A Rational number is a number which can be expressed in the form of $\dfrac{p}{q}$,where p and q are any integer value and q is not equal to 0. Such a number is known as a rational number.Don’t forget to cross check your result.The value which we divide is known as dividend. The value by which we divide is known as divisor.