Question

Find whether it is a terminating or non-terminating decimal
$3.2 \div 2.24$

Answer 1

Here the question is related to the decimal topic. We have to divide the given decimal number. To divide first we need to make the given number as the whole number because to make division easier i.e., multiply 3.2 by 100 and 2.24 by 100. After the division if we get the remainder as 0 then we consider it as a terminating decimal otherwise we are considering it as a non-terminating decimal. To divide the number we should know the tables of multiplication.

Complete answer:
To solve this first we know the definition of terminating and non-terminating decimals.
The number which has a finite number of digits after the decimal point is referred to as a terminating decimal.
The number which doesn’t have a finite number of digits after the decimal point is referred to as a non-terminating decimal.
Now we consider the given question
$3.2 \div 2.24$
This can be written in the form of fraction
$\Rightarrow \dfrac{{3.2}}{{2.24}}$
The number which is in the denominator is in the form of a decimal. So we multiply both numerator and denominator by 100. So we have
$\Rightarrow \dfrac{{3.2 \times 100}}{{2.24 \times 100}}$
On multiplying we have
$\Rightarrow \dfrac{{320}}{{224}}$
On dividing both numerator and denominator by 2 we have
$\Rightarrow \dfrac{{160}}{{112}}$
We can simplify for further
On dividing both numerator and denominator by 2 we have
$\Rightarrow \dfrac{{80}}{{56}}$
We can still simplify for further
On dividing both numerator and denominator by 8 we have
$\Rightarrow \dfrac{{10}}{7}$
There is no common number which can be divided both numerator and denominator
So on dividing the number 10 by 7 we have
$7\overset{1.428...}{\overline{\left){\begin{aligned} & {10} \\\ & \underline{7} \\\ & 30 \\\ & \underline{28} \\\ & 20 \\\ & \underline{14} \\\ & 60 \\\ & \underline{56} \\\ & 4 \\\ \end{aligned}}\right.}}$
So, after the decimal point we don’t have a finite number
therefore $3.2 \div 2.24$ is a non-terminating decimal.

Note:
While dividing the decimal number the student must and should know that the divisor should not be in the form of decimal. Suppose if it is in the decimal, we have to convert it into the whole number form by multiplying a number which has a power of 10. If the dividend is in the form of the decimal it does not matter.