Question

What per cent is $300g$ of $2kg$ ?

Answer 1

Hint: Notice that the units for both the quantities are different. So start with converting the unit in the same form, i.e. by using $1kg = 1000g$ . Now for finding the percent, calculate the fraction of quantity and then multiply it by hundred. Simplify it to find the required answer.

Complete step-by-step answer:
Here in this problem, we need to calculate what percent of $2kg$ is $300g$.
Before starting with the solution, let’s first understand the concept of percentage. In mathematics, a percentage is a number or ratio expressed as a fraction of hundred. It is often denoted using the percent sign, $'\% '$ , although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.
Notice that the given quantities are not in the same unit. For being unitless, the fraction’s numerator and denominator should be in the same units.
As we know that one kilogram is equal to a thousand grams, i.e. $1kg = 1000g \Rightarrow 2kg = 2000g$
Per cent can be calculated by finding the fraction of the quantities and then multiplying it by a hundred.
$ \Rightarrow \dfrac{{300}}{{2000}} \times 100$
Now this can be simplified by dividing both numerator and denominator by a hundred
$ \Rightarrow \dfrac{3}{{20}} \times 100$
As we can see that the number in denominator is a factor of hundred, so we get:
$ \Rightarrow \dfrac{3}{{20}} \times 100 = 3 \times 5$
Therefore, we get the percentage as $3 \times 5 = 15\% $
Hence, we calculated that the $300g$ of $2kg$ is $15\% $.

Note: In questions like this, always be careful with the units given of the quantities. A per cent is a ratio whose second term is 100. Percent means parts per hundred. The word comes from the Latin phrase per centum, which means per hundred. In mathematics, we use the symbol % for per cent. Do not forget to use this symbol while writing the final answer.