Problem 63 - Prealgebra

Question

Write as a percent. Round to the nearest tenth of a percent. $$\frac{83}{100}$$

Step-by-Step Solution

Answer

The fraction \( \frac{83}{100} \) is 83.0%.

Step 1: Understanding the Fraction

The given fraction is \( \frac{83}{100} \). When a fraction has a denominator of 100, it represents a percentage. This means the fraction represents how many parts out of 100, which is the definition of a percentage.

Step 2: Convert to Percent

To convert the fraction \( \frac{83}{100} \) to a percent, you simply interpret it as 83 parts out of 100, which is directly equal to 83%. This is because percentages are based on a whole of 100. So, \( \frac{83}{100} = 83\% \).

Step 3: Round to the Nearest Tenth of a Percent

Since \( 83 \% \) is already a whole number, it does not involve any decimal places to round. Thus, \( 83\% \) remains unchanged and rounds to 83.0% to the nearest tenth of a percent.

Key Concepts

Fractions to Percentages

Converting fractions to percentages is a fundamental concept in mathematics that lets you easily compare parts of a whole. The beauty of using percentages is that they convert any portion into out of 100, which is universally easy to understand. When you see a fraction like \( \frac{83}{100} \), it's particularly simple, as the denominator is already 100. This directly translates to a percentage value.

The process is straightforward:

• Check the fraction's denominator. If it's 100, the numerator is your percentage. So, \( \frac{83}{100} \) equals 83%.
• If the denominator isn’t 100, you can multiply both the numerator and denominator to convert it into a fraction with a denominator of 100. Then, interpret the numerator as the percentage.

If you're dealing with a more complex fraction, employ multiplication to turn it into a fraction over 100, making percentage conversion a breeze.

Rounding Decimals

Rounding decimals ensures that numbers are easy to read and work with, especially when precision isn’t paramount. When rounding percentages, particularly to the nearest tenth, you're adjusting the number to one decimal place.

Here’s how rounding is done:

• Identify the decimal digit that is in one-tenth position (first digit after the decimal point).
• If you were rounding 83% like in our example, and needed a decimal, placing a '.0' makes it 83.0%.

For numbers needing rounding:

• If the next decimal is 5 or more, round up the tenth's digit.
• If it’s less than 5, keep the tenth's digit as is.

While in this example, since 83 is a whole number, appending a zero and stating it as 83.0% personalizes it for rounding purposes without changing its value.

Basic Arithmetic

Basic arithmetic is the backbone of many math concepts and lays the foundation for more advanced topics. It involves fundamental operations like addition, subtraction, multiplication, and division. When working with percentages, understanding these operations is crucial.

Multiplication is vital in converting fractions when they don’t have a denominator of 100. For example:

• Given a fraction like \( \frac{4}{5} \), convert it by multiplying both the numerator and the denominator by 20 to make the fraction \( \frac{80}{100} \).
• This multiplication turns the fraction easily into a percentage: 80%.

If subtraction or addition are needed:

• Use subtraction to find how much a part fills up to a full percentage from an initial value.
• Addition helps in cumulative percentage calculations when percentages are combined.

These operations help in simplifying fractions, solving numeric problems, and making numeric sense of real-world situations.