Problem 73 - Prealgebra

Question

Write as a percent. Round to the nearest tenth of a percent. $$\frac{1}{6}$$

Step-by-Step Solution

Answer

\( \frac{1}{6} \) as a percent, rounded to the nearest tenth, is 16.7%.

Step 1: Convert Fraction to Decimal

To convert the fraction \( \frac{1}{6} \) to a decimal, divide the numerator by the denominator. Perform the division: \( 1 \div 6 \approx 0.1667 \).

Step 2: Convert Decimal to Percent

To convert a decimal to a percent, multiply the decimal by 100. Using the decimal from Step 1, calculate: \( 0.1667 \times 100 = 16.67 \).

Step 3: Round to the Nearest Tenth of a Percent

Round \( 16.67 \) to the nearest tenth of a percent. Look at the hundredths place (7), which means we round up the tenths place to get \( 16.7 \).

Key Concepts

Fraction to Decimal

This process involves converting a fraction into its decimal form. A fraction consists of a numerator and a denominator. To convert a fraction like \( \frac{1}{6} \) into a decimal, divide the numerator (1) by the denominator (6). You perform a division to get approximately \( 0.1667 \).

Here's a quick tip when converting fractions to decimals:

• Use a calculator for quick and precise division, especially if the fraction does not convert neatly.
• Understanding long division could also be helpful, especially for dealing with repeating decimals.

Through conversion, you make the fraction easier to work with, especially when further arithmetic operations are required. Decimals are used in many real-world applications due to their familiarity and ease of use.

Decimal to Percent

Once you have a decimal, the next step is converting it into a percent. Converting decimals to percents is simple: multiply the decimal number by 100. This is equivalent to moving the decimal point two places to the right.

For example, the decimal \( 0.1667 \) becomes \( 16.67 \% \).

Why do we multiply by 100? Because 'percent' means 'per hundred'. You're essentially calculating how many parts out of 100 your number represents:

• Decimals express parts of a whole based on powers of ten.
• Percents express parts of a whole per 100 units.

Converting decimals to percents is essential in everyday statistics, probabilities, and various forms of data interpretation.

Rounding Decimals

The concept of rounding is critical, especially when precision is necessary, but exact values are either unnecessary or impractical. Rounding to the nearest tenth involves looking at the digit in the hundredths place to decide whether the tenths place rounds up or stays the same.

In the case of \( 16.67 \% \), the hundredths digit is 7. Because this digit is greater than or equal to 5, the tenth digit (6) rounds up to 7, giving you \( 16.7 \% \).

Here are some useful tips for rounding:

• If the digit in the hundredths place is 5 or more, round up the tenths place by one.
• If the digit is less than 5, keep the tenths place the same.

Rounding provides a cleaner, easier-to-understand number, which is crucial in reports and when communicating with others about data.