Question

How do you change \[\dfrac{9}{24}\] into a decimal?

Answer 1

Hint: This question belongs to the topic of algebra. In this question, first we will multiply and divide the term \[\dfrac{9}{24}\]by 100, so that we will get the division in decimal form easily. After that, we will divide 9 multiplied by 100 by 24. After getting a new number by dividing, we will divide that new number by 100. After that, we will get the solution.

Complete step by step answer:
Let us solve this question.
In this question, we will find the decimal form of \[\dfrac{9}{24}\]. Or, we can say we have to simplify the term \[\dfrac{9}{24}\].
For changing the term \[\dfrac{9}{24}\] in decimal form easily, we will multiply 100 in both numerator and denominator.
So, the term \[\dfrac{9}{24}\] can also be written as
\[\dfrac{9}{24}=\dfrac{9}{24}\times \dfrac{100}{100}\]
As we know that using prime factorization, we can write
\[9=3\times 3\] ;
\[100=2\times 2\times 5\times 5\] ;
And
\[24=2\times 2\times 2\times 3\]
So, the above equation can also be written as
\[\Rightarrow \dfrac{9}{24}=\dfrac{3\times 3}{2\times 2\times 2\times 3}\times \dfrac{2\times 2\times 5\times 5}{100}\]
We can write the above equation as
\[\Rightarrow \dfrac{9}{24}=\dfrac{3}{2}\times \dfrac{5\times 5}{100}=\dfrac{3\times 5\times 5}{2\times 100}\]
As we know that the value of \[3\times 5\times 5\]is\[3\times 25\].
So, the above equation can also be written as
\[\Rightarrow \dfrac{9}{24}=\dfrac{3\times 25}{2\times 100}\]
We know that, if we divide 3 by 2, we get 1.5
So, we can write the above equation as
\[\Rightarrow \dfrac{9}{24}=\dfrac{3}{2}\times \dfrac{25}{100}=1.5\times \dfrac{25}{100}\]
Now, if we multiply 1.5 by 25, we get 37.5
Hence, the above equation can also be written as
\[\Rightarrow \dfrac{9}{24}=\dfrac{37.5}{100}\]
As we know that if the denominator has the term 10 to the power of n, where n is positive. Then, after removing the term of 10 to the power n, the decimal in the numerator shifts to the left side by n.
So, we can write the above equation as
\[\Rightarrow \dfrac{9}{24}=0.375\]

Hence, the decimal form of \[\dfrac{9}{24}\] is \[0.375\].

Note: We should have a proper knowledge in algebra to solve this type of question easily. We should know how to divide the numbers for solving this type of question. We can solve this question by alternate method.
The term \[\dfrac{9}{24}\] can also be written as
\[\Rightarrow \dfrac{9}{24}=\dfrac{3\times 3}{2\times 2\times 2\times 3}\]
The above equation can also be written as
\[\Rightarrow \dfrac{9}{24}=\dfrac{3}{2\times 2\times 2}\]
Here, we can see that there is only 2 in the denominator, then we will make the denominator as power of 10 by multiplying the denominator and numerator by 5 three times.
So, we can write the above equation as
\[\Rightarrow \dfrac{9}{24}=\dfrac{3\times 5\times 5\times 5}{2\times 2\times 2\times 5\times 5\times 5}\]
The above equation can also be written as
\[\Rightarrow \dfrac{9}{24}=\dfrac{375}{1000}\]
The above equation can also be written as
\[\Rightarrow \dfrac{9}{24}=0.375\]
Hence, from here also we get the same answer. So, we can use this method also to solve this type of question.