Question

How do you write \[\dfrac{3}{7}\] as decimal ?

Answer 1

Hint: In the above question you were asked to convert \[\dfrac{3}{7}\] as decimal. We know that for the decimal, the numerator should be divided by the denominator completely and the obtained solution will be the converted decimal number. So let us see how we can solve this problem by dividing numerator value 3 by the denominator value 7.

Complete step by step solution:
Here the given fraction is a proper fraction because the value in the numerator is less than the denominator as we can see 3 is smaller than 7.
In the given question we were asked to convert \[\dfrac{3}{7}\] into decimal.
So \[\dfrac{3}{7}\] in decimal can be calculated as below,
\[7\overset{0.4285}{\overline{\left){\begin{align}
  & 30 \\
 & \underline{28} \\
 & 020 \\
 & \underline{014} \\
 & 0060 \\
 & \underline{0056} \\
 & 00040 \\
 & \underline{00035} \\
 & 00005 \\
\end{align}}\right.}}\]
When we divide 3 by 7, we get the quotient as 0.4285 and with a remainder of 5. But we can further divide this fraction to achieve more decimal points as this is a non terminating value.
We can write the given fraction \[\dfrac{3}{7}\] as 0.4285 \[\approx \] 0.429
The value obtained is rounded off to three decimal places as shown above.

Note: To convert a number from the fraction part to decimal point it is necessary to divide the numerator by denominator. Also, note that when a fraction is solved we always get a decimal number. In the above solution, it is a proper fraction because the numerator is smaller than the denominator. If the decimal obtained is non terminating then we are supposed to round it off to three decimal points.