Question

How do you convert \[49/121\] into a decimal and percent?

Answer 1

Hint: We are given a fraction which we have to convert into a decimal and percent as well. We can see that the fraction cannot be reduced further, so we will simply divide 49 by 121. We will get the decimal form of the given fraction as the quotient. Now, to find the percent we will multiply the decimal equivalent of the given fraction by 100. Hence, we have the decimal equivalent as well as the percent equivalent of the given fraction.

Complete step-by-step answer:
According to the given question, we are given a fraction which we have to express in decimal form and percent form.
Decimal form involves numerals with a decimal point in it. In our calculations, we will find the decimal form up to two or three decimal places.
For example - \[0.123\], \[0.21\], etc.
Percent form is the representation of a specific quantity or amount for every hundred.
For example - \[50\%\], \[75\%\], etc.

The fraction given to us in the question is,
\[\dfrac{49}{121}\]----(1)
We can see that the fraction is not reducible and that we cannot make the denominator a multiple of 10. So, we will carry out the division of 49 by 121. We get,
\[121\overset{0.4049}{\overline{\left){\begin{align}
  & 49 \\
 & \underline{-0} \\
 & 490 \\
 & \underline{-484} \\
 & 600 \\
 & \underline{-484} \\
 & 1160 \\
 & \underline{-1089} \\
 & \_\underline{71}\_ \\
\end{align}}\right.}}\]

The quotient that we obtained after dividing the fraction is in the decimal form and also it has decimal point.
So, \[\dfrac{49}{121}=0.4049\approx 0.405\]
To find the percent, we will straightaway multiply the decimal form, that we calculated, by 100.
We have,
\[0.4049\times 100=40.49\%\]
Therefore, the decimal equivalent is \[0.405\] and the percent equivalent is \[40.49\%\].

Note: The quotient that we obtained was \[0.4049\] but we wrote the final answer as \[0.405\]. This is called rounding off. It is based on how many decimal places we require. We took three places of decimal, that is why we wrote the answer as \[0.405\]. If we want two places of decimal then, the answer will be \[0.40\].