Problem 57 - Prealgebra

Question

Change each fraction or mixed number to a percent. $$\frac{1}{3}$$

Step-by-Step Solution

Answer

\(\frac{1}{3} = 33.33\%\)

Step 1: Understand the fraction

Recognize that the fraction \( \frac{1}{3} \) represents a part of a whole, where 1 is the numerator and 3 is the denominator.

Step 2: Convert fraction to decimal

Convert the fraction \( \frac{1}{3} \) into a decimal by performing the division \( 1 \div 3 \). This gives approximately \( 0.3333 \).

Step 3: Convert decimal to percent

Convert the decimal \( 0.3333 \) to a percent by multiplying it by 100. This means \( 0.3333 \times 100 = 33.33 \).

Step 4: Round the percent

Round the percent to a reasonable decimal place if necessary. Here, \( 33.33 \% \) is already a common rounding for a repeating decimal.

Key Concepts

Fraction to Decimal Conversion

Converting a fraction to a decimal is like translating between two languages of numbers. A fraction like \( \frac{1}{3} \) is a way of expressing numbers showing a part of a whole. You have one part out of three equal parts. To convert it to a decimal, you perform division. Specifically, you divide the numerator (1) by the denominator (3).
- Perform the division: \( 1 \div 3 \).- This results in a repeating decimal \( 0.3333 \), where the 3 goes on indefinitely.Repeating decimals have a pattern. Here, the digit 3 repeats forever, noted as \( 0.\overline{3} \). Understanding this conversion is crucial in math because decimals are often more user-friendly for calculations compared to fractions.

Decimal to Percent Conversion

Converting decimals to percents is straightforward. Think of percents as the decimal moved to a base of 100. The word 'percent' comes from the Latin 'per centum', meaning 'by the hundred'. Here’s how you convert:
- Take the decimal \( 0.3333 \).- Multiply by 100: \( 0.3333 \times 100 = 33.33 \).You’re essentially shifting the decimal place two steps to the right. This transformation makes it easy to express fractions as a part of 100, which is often more intuitive to understand as humans are very used to thinking in terms of percentages.

Rounding Decimals

Rounding is the process of simplifying a number to make it easier to handle. When you have a repeating decimal, like \( 0.3333 \), it might make calculations easier to use a rounded version. This is managed by looking at the digit just past the place you are rounding to, helping you decide whether to round up or keep the number the same.
- Look at \( 0.3333 \) and decide on a place to round, often to the hundredth place.- If rounding \( 0.3333 \), you end up with \( 0.33 \).Since percent conversion led us to \( 33.33\% \), we chose a typical two-digit rounding strategy. This is widely used, making it a standard way to present repeating decimals succinctly. Rounding like this helps in making concise, readable numbers, especially when dealing with decimal to percent conversions.