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Chapter 7: Problem 5

Convert the fraction to a percent. $$\frac{3}{8}$$

Short Answer

Expert verified
37.5%

Step by step solution

01

- Convert Fraction to Decimal

To convert the fraction \(\frac{3}{8}\) to a decimal, divide the numerator (3) by the denominator (8). Calculate \( \frac{3}{8} = 0.375 \).
02

- Convert Decimal to Percent

To convert the decimal 0.375 to a percent, multiply by 100. \(0.375 \times 100 = 37.5\).
03

- Write Final Answer as Percent

The final answer is \(37.5\%\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

fraction to decimal conversion
Converting a fraction to a decimal involves a simple division. The fraction, such as \( \frac{3}{8} \), represents a division problem. Here, the numerator (3) is divided by the denominator (8). Doing this, \( \frac{3}{8} \) gets converted to 0.375. This means that \( \frac{3}{8} = 0.375 \).

Understanding fractions and decimals is crucial as they are often interchangeable in mathematics. Here's an easy way to look at it:
  • Fractions are ways of expressing parts of a whole.
  • Decimals are another form of expressing those same parts of a whole.
So, to recap: always divide the numerator by the denominator to change a fraction into a decimal.
decimal to percent conversion
Once a decimal like 0.375 is obtained, converting it to a percent is straightforward. To do so, multiply the decimal by 100.

Here's the process: 0.375 multiplied by 100 equals 37.5.

So why multiply by 100? The reason is that 'percent' means 'per hundred'. Therefore, moving the decimal point two places to the right (or multiplying by 100) gives us the percent value.
  • 0.375 becomes 37.5%
This method works for any decimal number, making it easy to switch back and forth between decimals and percentages.
basic arithmetic operations
Basic arithmetic operations like division and multiplication form the foundation of converting fractions to percents.

For the given problem, we used division to go from a fraction to a decimal and multiplication to transition from a decimal to a percent. Well understanding these operations is key:
  • Division: Used to convert fractions to decimals.
  • Multiplication: Used to convert decimals to percentages.

In our example, we performed these steps effectively:
  • \( \frac{3}{8} = 0.375 \) using division.
  • 0.375 x 100 = 37.5% using multiplication.

Understanding these operations makes math problems easier and helps convert between different mathematical representations seamlessly.

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Most popular questions from this chapter

Which of the numbers represent \(60 \% ?\) a. 6.0 b. \(0.60 \%\) c. 0.6 d. \(\frac{3}{5}\)

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{5}{11}$$

Solve the problem using a percent equation. What percent of 25 is \(18 ?\)

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