Problem 29 - Prealgebra

Question

Express each percent as a fraction or mixed number in simplest form and as a decimal. $$0.53 \%$$

Step-by-Step Solution

Answer

0.53% is \( \frac{53}{10000} \), which is 0.0053 as a decimal.

Step 1: Write the Percentage as a Fraction

Start by expressing the percentage as a fraction. A percentage is a value out of 100, so 0.53% can be written as \( \frac{0.53}{100} \).

Step 2: Convert to Decimal Form

To find the decimal equivalent, divide the percentage by 100. So, \(0.53\%\) becomes \( \frac{0.53}{100} = 0.0053\).

Step 3: Simplify the Fraction

Convert the fraction \( \frac{0.53}{100} \) into a simpler form by eliminating the decimal point, resulting in \( \frac{53}{10000} \), since 0.53 is the same as \( \frac{53}{100} \). Then, check if the fraction can be simplified. Here, it is already in simplest form.

Key Concepts

Simplifying Fractions

Understanding how to simplify fractions is a key math skill that helps reveal the simplest form of a fraction. A fraction consists of a numerator (the top number) and a denominator (the bottom number). To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).

• Find the GCD of the numerator and the denominator.
• Divide both the numerator and the denominator by this GCD.
• Ensure that the resulting fraction cannot be simplified further.

This way of simplifying reduces the fraction to its most basic form, where the numerator and denominator share no common divisors other than 1. For example, \(\frac{8}{12}\) becomes \(\frac{2}{3}\) after simplification, because 4 is the GCD of 8 and 12.

In our example, when we have \(\frac{53}{10000}\), it is already in simplified form because 53 and 10000 have no common divisors other than 1.

Decimal to Fraction Conversion

Converting a decimal to a fraction involves a few straightforward steps. Start by writing down the decimal divided by 1, which will form the base of your fraction conversion.

• Multiply the numerator and the denominator by 10 for every digit after the decimal point.
• In our case, the decimal 0.53 has two digits after the decimal point, so we multiply by 100, giving us \(\frac{53}{100}\).
• Once you have your fraction, check if it can be simplified further by finding the GCD, as discussed earlier.

This process transforms your decimal into a clear and simple fraction form which is easier to interpret and use in further calculations. The conversion of decimals to fractions is a useful skill in various real-world contexts, like in finance and measurements.

Percentage Calculation

Percentage calculation is an essential skill in math that helps quantify parts per 100. The term "percent" is derived from "per centum," meaning "by the hundred." To convert a percentage to a fraction:

• Write the percentage number over 100.
• For instance, 0.53% becomes \(\frac{0.53}{100}\).
• Then, convert the fraction to remove any decimals, resulting in \(\frac{53}{10000}\).
• Finally, simplify the fraction if possible.

This process transforms a percentage into a format that might be more useful for different mathematical operations. Calculating percentages is critical as it is widely used in contexts such as statistics, finance, and academic grading.