Question

What percent of \[1km\] is \[100 \text{meters}\]?

Answer 1

Hint: We are given a value and we are asked to find as to what percentage of \[1km\] is the given value. First of all, we will make sure all the given values are in the same units. We know that one kilometre is equal to 1000 meters. We will let the unknown percent be \[x\%\]. Then, we will write the appropriate mathematical expression for the given statement in the question and we have it as, \[x\%\times 1km=100meters\]. We will solve this expression in terms of ‘x’ and find the value of the ‘x’. hence, we will have the required per cent.

Complete step-by-step solution:
According to the given question, we are given a value \[100meters\] and we are asked to find the percentage equivalent of \[1km\] that gives this value.
Firstly, we have to note that all the values are in the same units. We know that, one kilometre contains 1000 meters, we will be using this conversion in the calculation.
Let the unknown percent be \[x\%\]
Next, we will write the appropriate mathematical expression for the given statement in the question and we get the expression as,
\[x\%\times 1km=100meters\]
Now, opening up the expression, we have,
\[\Rightarrow x\%\times 1000meters=100meters\]
We will now solve for ‘x’ and we get,
\[\Rightarrow \dfrac{x}{100}\times 1000=100\]
We will now remove the similar terms and we get the new expression as,
\[\Rightarrow x\times 10=100\]
\[\Rightarrow 10x=100\]
Writing the expression in terms of ‘x’, we get the value of ‘x’ as,
\[\Rightarrow x=\dfrac{100}{10}\]
\[\Rightarrow x=10\%\]
Therefore, \[10\%\] of \[1km\] is \[100meters\].

Note: While writing the mathematical expression for the statement given in the question, make sure that the values don’t get interchanged. As then the question itself will get changed. If we write, \[x\%\times 100m=1km\], it would mean that we are finding the percent of 100 meters that will give rise to 1 kilometre, basically the reverse of the question asked.