Problem 82 - Prealgebra

Question

Write as a percent. Write the remainder in fractional form. $$\frac{12}{25}$$

Step-by-Step Solution

Answer

48% (no remainder)

Step 1: Convert Fraction to Decimal

We begin by converting the fraction \( \frac{12}{25} \) into a decimal. Divide the numerator by the denominator: \( 12 \div 25 = 0.48 \).

Step 2: Convert Decimal to Percent

To convert the decimal to a percent, multiply by 100: \( 0.48 \times 100 = 48 \% \).

Step 3: Verify Whole Part and Fractional Remainder

Since \( 0.48 \) converts directly to 48% without a remainder, there is no need for a fractional remainder. The conversion is exact.

Key Concepts

Fraction to Decimal Conversion

Converting a fraction into a decimal is a foundational skill in mathematics that helps to simplify calculations and comparisons. To transform a fraction, like \( \frac{12}{25} \), into a decimal, you divide the numerator (the top number) by the denominator (the bottom number). In this case, you would perform the division: \( 12 \div 25 \), which gives you \( 0.48 \).
This method works because division is essentially a way of determining how many parts of the denominator fit into the numerator. Understanding this will help in handling large denominators and numerators efficiently.
Remember that division might sometimes result in a repeating decimal. However, for fractions where the denominator is a factor of 10 or 100, like in our example \( \frac{12}{25} \), conversion will often result in a finite decimal.

Decimal to Percent Conversion

Once a fraction is converted to a decimal, turning that decimal into a percent is straightforward. A percent represents parts per hundred, so you multiply the decimal by 100. This action shifts the decimal point two places to the right, transforming the decimal frequently into a whole number.
For instance, when you have \( 0.48 \), multiplying by 100 gives you \( 48 \). Therefore, \( 0.48 \) as a percent is \( 48\% \).
This step is crucial not only for mathematics problems but also real-life scenarios like calculating discounts, interest rates, and statistics. A helpful reminder is that multiplying by 100 is equivalent to finding how many parts per 100 your decimal represents.

Exact Conversion

Exact conversion refers to transforming numbers with precision, ensuring there's no approximation involved. In our example, when converting \( \frac{12}{25} \) to a percent, the outcome \( 48\% \) is exact.
An exact conversion is special because it shows a whole number percent without any decimals or fractions remaining. This can happen when the decimal conversion perfectly aligns with a whole percent.
Understanding when an exact conversion is possible helps in mathematical accuracy and simplifies the communication of data. Remember, verifying your conversions, as shown in the example, assures that there is no error or remainder, solidifying the accuracy of your results.