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Magazine Chapter 7: Problem 42
Solve.What percent of 500 is \(3 ?\)
Short Answer
Expert verified
3 is 0.6% of 500.
Step by step solution
01
Understand the Problem
We need to find out what percent 3 is of 500. This involves finding the ratio of 3 to 500 and then converting that ratio into a percentage.
02
Set Up the Fraction
Express the relationship between 3 and 500 as a fraction: \( \frac{3}{500} \). This fraction represents the part of 500 that 3 is.
03
Convert the Fraction to a Decimal
To convert the fraction \( \frac{3}{500} \) to a decimal, divide 3 by 500 using a calculator or long division: \[ \frac{3}{500} = 0.006 \]
04
Convert the Decimal to a Percentage
To convert the decimal 0.006 to a percentage, multiply by 100:\[ 0.006 \times 100 = 0.6 \% \] Thus, 3 is 0.6% of 500.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding Fractions
Fractions are a way to represent parts of a whole. They consist of two numbers: the numerator (top number) and the denominator (bottom number). In the fraction \( \frac{3}{500} \), 3 is the numerator, which tells us the amount we're considering, while 500 is the denominator, indicating the total amount.
- The numerator shows how many equal parts are being counted.
- The denominator shows the total number of equal parts the whole is divided into.
Converting Decimals
Decimals are another method to convey fractions in a simplified form. When you divide the numerator by the denominator in a fraction, you convert it into a decimal. For the fraction \( \frac{3}{500} \), the division yields 0.006.
- Decimals often make calculations easier, especially in comparison and addition of values.
- They are essential in expressing numbers that aren't whole in a more flexible and understandable way.
Ratios in Percentages
A ratio compares two quantities, showing the relationship between them. It鈥檚 foundational in transforming a question into understandable parts. In our example, the ratio is \( \frac{3}{500} \). By expressing this ratio, we can see how one number relates to another, paving the way for easy conversion into percentages.
- Ratios are usually expressed in fraction form to give a clear picture of part-to-whole relationships.
- They simplify understanding how one quantity stacks up against another.
Mathematical Problem Solving with Percentages
Problem-solving in math can be mostly about knowing which steps to take. In this case, finding what percent of 500 is 3 involves a few clear operations: setting up a fraction, converting it to a decimal, and then to a percentage. These steps capitalize on our understanding of fractions, decimals, and ratios.
- First, translate the problem into a fraction to decipher the relationship.
- Next, compute a decimal to measure the specific part of the whole.
- Finally, translating the decimal into a percentage makes it easier to understand and communicate.
