Question

What percent of $$36.3 \text { is } 12.7 ?$$

Short answer

12.7 is approximately 35% of 36.3.

Step-by-step solution

Identify the Values

Identify the 'whole' and the 'part' from the question. The 'whole' is 36.3, and the 'part' we want to find the percentage of is 12.7.

Write the Percentage Formula

The formula to calculate percentage is: \( \frac{\text{part}}{\text{whole}} \times 100 \).

Plug in the Values into the Formula

Replace 'part' with 12.7 and 'whole' with 36.3 in the formula, which gives: \( \frac{12.7}{36.3} \times 100 \).

Calculate the Division

Divide 12.7 by 36.3 to get: \( \frac{12.7}{36.3} = 0.3498... \).

Multiply by 100 for Percentage

Multiply the result by 100 to convert it to a percentage: \( 0.3498... \times 100 = 34.98...\% \).

Round to a Suitable Decimal Place

Round the percentage to two decimal places if necessary, which gives approximately 35%.

Key concepts

Percentage Formula

When we talk about the percentage formula, it's essentially a mathematical way to express a number as a fraction of 100. This is incredibly useful in various fields, from calculating discounts on your shopping spree to determining what portion of a pie chart you're looking at in a business presentation. The formula is quite straightforward:

\textbf{Percentage} = \( \frac{\text{part}}{\text{whole}} \times 100 \).

The 'part' represents the portion of the 'whole' for which you are seeking the percentage. To translate this idea into a crisp, clear process, imagine you have 36.3 apples, and you want to know what percentage 12.7 of those apples make up. By applying the formula, you starkly clarify the relationship between the 'part' and the 'whole,' which is at the essence of percentage calculations.

Mathematical Reasoning

Understanding Through Context

Decoding a problem using mathematical reasoning involves more than just applying formulas; it's about understanding how and why the formula works. Let's delve into the previous example where you're tasked to find what percent 12.7 represents out of 36.3. Here, reasoning guides us to perceive 12.7 as a fragment of 36.3. By metricizing this relationship with the percentage formula, you see the comparative size and discover that 12.7 constitutes a significant portion of 36.3.

With mathematical reasoning, you also appreciate the necessity to round the final answer to avoid impractical, overly precise percentages which are not user-friendly in real-life situations—thus the rounding to 35%. This encapsulates the importance of viewing and utilizing numbers as tools to quantify and compare, which is an indispensable skill in making well-informed decisions.

Fraction to Percentage Conversion

From Fraction to Clarity

Converting a fraction to a percentage is a critical skill and quite a simple one once you grasp the core concept. It all boils down to recognizing a percentage as a fraction with a denominator of 100. Here's a relatable way to digest this concept: if you slice a cake into 100 equal pieces, each slice represents a 1% share of the cake. So, when you're converting a fraction like \( \frac{12.7}{36.3} \) to a percentage, you're essentially figuring out how many slices of a 100-slice cake you would get if a whole cake represented 36.3.

In mathematical terms, you’re scaling up the original fraction to out of 100 by multiplying it by 100. That pivotal multiplication flips the fraction \( \frac{12.7}{36.3} \) into the percentage 34.98%, which, for practicality and ease of comprehension, is rounded up to 35%. The beauty of converting fractions to percentages is that it renders fractions, which can be abstract, into tangible percentages that are simpler to visualize and use.