Problem 62 - Prealgebra

Question

Write as a percent. Round to the nearest tenth of a percent. $$\frac{27}{50}$$

Step-by-Step Solution

Answer

54.0%

Step 1: Convert fraction to decimal

To convert the fraction \( \frac{27}{50} \) into a decimal, divide the numerator by the denominator: \( 27 \div 50 = 0.54 \).

Step 2: Convert decimal to percent

To convert the decimal \( 0.54 \) into a percentage, multiply it by 100: \( 0.54 \times 100 = 54 \).

Step 3: Round the percent

Since the percent is already a whole number and rounding to the nearest tenth means checking the first decimal place, 54 remains 54.0%.

Key Concepts

Converting Fractions to Decimals

Understanding how to convert fractions to decimals is a foundational math skill. It involves dividing the top number (numerator) by the bottom number (denominator). This process can be thought of as finding out how many times the denominator will "fit" into the numerator.

For instance, with the fraction \( \frac{27}{50} \), you perform a simple division: \( 27 \div 50 \). Since 50 cannot "fit" into 27 as a whole number, the division will yield a result less than 1, specifically 0.54. This decimal tells you that \( 27 \) is 54% of the way to \( 50 \).

Remember, fractions that have numerators smaller than the denominators (like our example) will always result in decimals less than 1.

Rounding to the Nearest Tenth

Once you have converted a fraction to a decimal, you might need to round it to a certain place value. Rounding to the nearest tenth involves looking at the number in the hundredths place (the second digit after the decimal point), and deciding whether it rounds up or stays the same.

Consider the decimal 54. Here, there is no digit after the decimal. If our result had been something like 54.36, we would look at the 6 in the hundredths place to determine our rounding. If this number is 5 or more, we round up the tenths place by 1. Thus, 54.36 would round to 54.4. However, since our example was a whole number, we technically had 54.0, which stays as it is.

Rounding is especially useful when further calculations or readability requires a simpler form.

Basic Arithmetic Operations

Performing basic arithmetic operations is crucial for many everyday tasks and more advanced mathematical problems. Operations such as addition, subtraction, multiplication, and division form the cornerstone of arithmetic.

In the context of converting fractions to decimals, division is the primary operation. As seen with \( \frac{27}{50} \), division helps us convert the fraction into the decimal 0.54. Without understanding division, this conversion would be challenging.

Additionally, multiplication is used when converting decimals to percentages. We multiply the decimal by 100 since a percentage is the number of parts per 100. So, taking 0.54 and moving to 54% involves multiplying by 100, effectively shifting the decimal point two places to the right.

Mastering these operations allows for greater mathematical fluency and precision, whether you’re working through textbook exercises or real-world scenarios.