Problem 60 - Prealgebra

Question

Change each fraction or mixed number to a percent. $$\frac{1}{6}$$

Step-by-Step Solution

Answer

\(\frac{1}{6}\) is approximately 16.67%.

Step 1: Understand the Basics

To convert a fraction to a percent, you need to multiply the fraction by 100, since a percent is essentially a number out of 100.

Step 2: Set Up the Expression

Write the expression to convert the fraction \(\frac{1}{6}\) into a percent: \(\frac{1}{6} \times 100\).

Step 3: Perform the Multiplication

Calculate the multiplication: \(\frac{1}{6} \times 100 = \frac{100}{6}\).

Step 4: Simplify to Decimal Form

Divide 100 by 6 to simplify the expression into decimal form: \(\frac{100}{6} \approx 16.6667\).

Step 5: Express as a Percent

Since 16.6667 is the decimal form, express it as a percentage which is approximately 16.67%. Notice the repeating decimal and round it to two decimal places for the percentage.

Key Concepts

Fraction Multiplication

To convert a fraction to a percent, we first need to understand the process of multiplying fractions. Fractions are expressed as a ratio of two numbers, like so: \( \frac{a}{b} \). When we want to multiply a fraction by a whole number, like 100 (since a percent is out of 100), it’s important to remember that we multiply the numerator and keep the denominator as is.

For example, if we have the fraction \( \frac{1}{6} \), to convert it to a percent, we multiply it by 100. This is written as \( \frac{1}{6} \times 100 \). Multiply the numerator by 100, so the expression becomes \( \frac{100}{6} \).

The process of multiplying fractions is straightforward, but ensuring you only multiply the top of the fraction keeps it accurate. This multiplication helps us move towards expressing the fraction in terms of a percentage.

Decimal Conversion

Decimal conversion is the next key step in moving from a fraction to a percentage. After multiplying the fraction by 100, you'll often get a number that still has a fraction—known as an improper fraction.

To convert \( \frac{100}{6} \) to a decimal, you perform division and calculate \( 100 \div 6 \). This equals approximately 16.6667. This step can initially seem daunting but is just about performing simple division to see how many times the denominator fits into the numerator.

• Divide as you would with any long division method.
• The result is your decimal.

Decimals make it easier to understand portions that fractions represent, mainly because we often consider parts of things in tens or hundreds, making decimals relatable.

Rounding Decimals

Rounding decimals is crucial when working with numbers that have many decimal places. Typically, when representing certain kinds of data, especially percentages, we round decimals to ensure clarity and simplicity.

After converting \( \frac{100}{6} \) to the decimal 16.6667, you must round it to the nearest hundredth to turn it into a standard percentage form: 16.67%.

• Look at the digit in the thousandths place.
• If it's 5 or greater, round the hundredths place up by one.
• If it's less than 5, keep the hundredths place as it is.

Rounding makes numbers more manageable and ensures they are presented in a reader-friendly way, which is vital for understanding data at a glance. By rounding, you turn complex decimals into easy-to-read numbers.