Question

What percent is : 25 cm of 4 meters ?

Answer 1

Hint: To find the percentage of 25 cm of 4 meters, we have to convert 4 meters into centimeters by multiplying 4 by 100 since 1 meter is 100 centimeters. Then, we have to find the percentage of 25 cm of 400 cm by dividing 25 by 400 and multiplying the result by 100.

Complete step by step solution:
We have to find the percentage of 25 cm of 4 meters. Let us convert 4 meters into centimeters. We know that 1 meter is 100 centimeters.
$\Rightarrow 1\text{ m}=100\text{ cm}$
Therefore, 4 meters will be 100 multiplied by 4.
$\begin{align}
  & \Rightarrow 4\text{ m}=100\times 4\text{ cm} \\
 & \Rightarrow 4\text{ m}=400\text{ cm} \\
\end{align}$
Now, we have to find the percentage of 25 cm of 400 cm. We know that to convert a number into percentage, we have to multiply it with 100. We can write this mathematically as
$\dfrac{25}{400}\times 100\%$
Let us cancel the zeroes from the numerator and the denominator.
$\Rightarrow \dfrac{25}{4\require{cancel}\cancel{0}\require{cancel}\cancel{0}}\times 1\require{cancel}\cancel{0}\require{cancel}\cancel{0}\%$
We can write the result of the above simplification as
$\Rightarrow \dfrac{25}{4}\%$
We can write the above fraction as a mixed fraction. For this, we will divide 25 by 4.
$4\overset{6}{\overline{\left){\begin{align}
  & 25 \\
 & -24 \\
 & \_\_\_\_ \\
 & \begin{matrix}
   {} & 1 \\
\end{matrix} \\
\end{align}}\right.}}$
We can write in mixed fraction as $\text{Quotient}\dfrac{\text{Remainder}}{\text{Divisor}}=6\dfrac{1}{4}$
Therefore, $\dfrac{25}{4}\%=6\dfrac{1}{4}\%$ .
We can also write $\dfrac{25}{4}\%$ in the decimal form.
\[4\overset{6.25}{\overline{\left){\begin{align}
  & 25.00 \\
 & -24 \\
 & \_\_\_\_\_\_ \\
 & \begin{matrix}
   {} & 10 \\
\end{matrix} \\
 & \begin{matrix}
   {} & -8 \\
\end{matrix} \\
 & \_\_\_\_\_\_ \\
 & \begin{matrix}
   {} & \text{ }\text{ }\text{ }20 \\
\end{matrix} \\
 & \begin{matrix}
   {} & \text{ }\text{ }\text{ }-20 \\
\end{matrix} \\
 & \_\_\_\_\_\_\_ \\
 & \begin{matrix}
   {} & {} & 0 \\
\end{matrix} \\
\end{align}}\right.}}\]
Therefore, $\dfrac{25}{4}\%=6.25\%$ .
Hence, 25 cm of 4 meters. is $\dfrac{25}{4}\%\text{ or }6\dfrac{1}{4}\%\text{ or }6.25\%$ .

Note: Students have a chance of writing 25 cm of 400 cm as $25\times 400$ . This leads to wrong results. Students have a chance of making a mistake when converting meters into centimeters by writing 1 cm as 100 meters.