Question

How do you write \[5\dfrac{3}{4} \div 23\] as a fraction and as a decimal number?

Answer 1

Hint: Here in this question, we simplify the given number by using the arithmetic operation division and we have to convert the given number into decimal. The given number is in the form of fraction, to convert the fraction number to the decimal we divide the given number by the number which is in the denominator. And then we obtain the required answer.

Complete step-by-step solution:
Now consider the number \[5\dfrac{3}{4} \div 23\], the first term is in the form of mixed fraction. so convert the mixed fraction into improper so we have
\[ \Rightarrow \dfrac{{23}}{4} \div 23\]
So it is written as
\[\dfrac{{\dfrac{{23}}{4}}}{{23}}\]
By taking reciprocal we get
\[ \Rightarrow \dfrac{{23}}{4} \times \dfrac{1}{{23}}\]
Since the number 23 present in the both numerator and denominator, it gets cancel
\[ \Rightarrow \dfrac{1}{4}\]

The number can be converted from one form to another. We have to convert the fraction number into a decimal number. The fraction is a proper fraction where the value of the numerator is less than the value of the denominator. We can’t divide the number 1 by the number 4. By taking the decimal point in quotient we can solve the problem. By decimal point we can carry the zero to the number.

Now consider the number \[\dfrac{1}{4}\], on applying division we have

When we take a decimal point in the quotient the number 1 will become 10. Then we can divide the number 10 by 4. On dividing ee get the remainder as zero. Hence, we have converted the fraction into the decimal number.

Therefore, the decimal form or value for the fraction number \[\dfrac{1}{4}\] is 0.25.

Note: The number can be converted from one form to the other form. For the conversion of numbers, we have some rule or method. By using the specific methods and rules we can convert the number. The fraction number has a numerator and denominator. The decimal number will have the decimal point. While conversion we use the arithmetic operations such as division and multiplication.