Question

4. While converting a fraction into decimal instead of dividing the numerator by the denominator, a
student divided the denominator by the numerator. If s/he got the answer as 0.625, then find the
correct decimal number for the fraction.
​

Answer 1

Answer:

The  correct decimal number for the fraction is 1.6

Step-by-step explanation:

Given :

• While converting a fraction into decimal instead of dividing the numerator by the denominator, a student divided the denominator by the numerator.
• S/he got the answer as 0.625

To find :

the  correct decimal number for the fraction

Solution :

Let the fraction be 'k'

 $\sf fraction=\dfrac{numerator}{denominator}$

Hence, k = numerator/denominator

A student divided the denominator by the numerator.

⇒ denominator/numerator

 $\sf k=\dfrac{numerator}{denominator} \\\\ \implies \sf \dfrac{denominator}{numerator}=\dfrac{1}{k}$

Hence, the student got the answer for the value of 1/k

The student got the answer as 0.625

So, 1/k = 0.625

   $\sf \dfrac{1}{k}=\dfrac{625}{1000} \\\\ \sf k=\dfrac{1000}{625} \\\\ \sf k= \dfrac{25 \times 40}{25 \times 25} \\\\ \sf k=\dfrac{40}{25} \\\\ \sf k=\dfrac{5 \times 8}{5 \times 5} \\\\ \sf k=\dfrac{8}{5} \\\\ \boxed{\bf k=1.6}$

Therefore, the  correct decimal number for the fraction is 1.6