Question

Write the fraction as a decimal and as a percent. $$ \frac{11}{20} $$

Short answer

The fraction \( \frac{11}{20} \) converted to a decimal is 0.55 and as a percent is 55%

Step-by-step solution

Convert Fraction to Decimal

To convert the fraction \( \frac{11}{20} \) to a decimal, divide the numerator (which is 11) by the denominator (which is 20). That gives, \( \frac{11}{20} = 0.55 \)

Convert Decimal to Percentage

To convert the obtained decimal value to a percent, multiply by 100. So, 0.55 times 100 equals 55, so we have 55%.

Key concepts

Fraction to Decimal Conversion

Understanding how to convert fractions to decimals is a fundamental skill that can simplify many math problems. Have you ever noticed that a fraction is very much like division? That's because it is! For example, to convert the fraction \( \frac{11}{20} \) into a decimal, you essentially perform the division of the numerator (11) by the denominator (20).

Here's a helpful tip: you can think of the line in a fraction as a division sign. So, when you have \( \frac{11}{20} \), just divide 11 by 20 to get 0.55. Reaching a decimal form is merely an execution of straightforward division, which can easily be done using a calculator or by hand if the numbers are simple enough.

Remember, some fractions may result in a long string of numbers after the decimal point. In such cases, we might round it off to make it more readable and understandable, depending on what the situation requires.

Decimal to Percent Conversion

Once you've mastered converting a fraction to a decimal, the next step is quite simple: turning that decimal into a percent. Percent means 'per hundred', and that is exactly what you do—multiply the decimal by 100.

For the decimal 0.55, you just multiply it by 100 to convert it to percent. Here's how it looks: \( 0.55 \times 100 = 55% \). It's like shifting the decimal point two places to the right. If you ever get stuck, remember that you're essentially counting how many times the decimal fits into 100. It’s a quick operation that can also be done without much effort. Voila, you have your percentage!

Numerical Operations

Numerical operations form the backbone of much of mathematics, and both fraction to decimal and decimal to percent conversions rely on these operations. With fractions, division is the key operation, as you divide the top number by the bottom. With decimals and percents, multiplication comes into play, especially when you're multiplying by 100 to find a percentage.

• Always pay attention to the order of operations; for example, handle parentheses first if they’re involved in your calculations.
• Use estimation to check the plausibility of your answers. If a fraction is slightly more than half, the decimal should be more than 0.5, and the percent should be more than 50%.
• For complex fractions or decimals, consider tools like fraction strips or decimal grids to visualize the process.

The combination of these foundational operations is not only critical for converting numbers from one form to another but also for problem-solving in everyday situations.