Problem 66 - Prealgebra

Question

Write as a percent. Round to the nearest tenth of a percent. $$\frac{5}{11}$$

Step-by-Step Solution

Answer

45.5%

Step 1: Convert the Fraction to Decimal

To convert the fraction \( \frac{5}{11} \) to a decimal, divide the numerator by the denominator. So, divide 5 by 11. The result is approximately 0.454545... which is a repeating decimal.

Step 2: Multiply by 100 to Convert to Percent

To convert a decimal into a percent, multiply the decimal by 100. Multiply 0.454545... by 100 to get approximately 45.4545... which is the percent value.

Step 3: Round to the Nearest Tenth of a Percent

The next step is to round 45.4545...% to the nearest tenth of a percent. Look at the hundredths place, which is a 5 (in 45.4545...). Since it is 5 or more, round the tenths place up from 4 to 5. So, the final result is 45.5%.

Key Concepts

Converting Fractions to Decimals

Converting a fraction to a decimal involves division. You take the top number (numerator) and divide it by the bottom number (denominator). For example, when converting \( \frac{5}{11} \), you divide 5 by 11. This process results in a decimal number.

• The division might give you an exact number, like 0.5, if the decimal terminates.
• Other times, it might result in a repeating decimal, like 0.454545..., which is what you get with \( \frac{5}{11} \).

Understanding how to perform this division accurately is key in math problems where decimals are needed. You can use a calculator for quick conversion or practice dividing manually for better comprehension.

Understanding Repeating Decimals

Repeating decimals occur when after dividing the numerator by the denominator, the digits start to repeat indefinitely. Observing the result of \( \frac{5}{11} \), we get 0.454545..., with "45" as the repeating sequence.

• Recognize the repeating pattern which typically appears after the decimal point.
• Sometimes, just the first few digits repeat, and sometimes longer sequences do.

In some cases, the repeating part is denoted by an overline, like 0.\(\overline{45}\). Knowing how to identify and work with repeating decimals helps in precise calculations and provides better insights into number properties.

Rounding Decimals

Rounding decimals is a way to simplify numbers by reducing the number of digits. In our example, we're rounding to the nearest tenth of a percent. This means looking at the hundredths place to decide if the tenths digit should round up.

• If the number in the hundredths place is 5 or more, increase the tenths place by one.
• If it is less than 5, keep the tenths place the same.

For 0.454545..., multiplying by 100 gives you 45.4545... which rounds to 45.5. Rounding helps in making data easier to read and look more professional by simplifying to a significant level.

General Math Problem-Solving Steps

Solving math problems efficiently involves a systematic approach:

• Understand the Problem: Clearly identify what you need to solve. Read the exercise requirements carefully.
• Plan Your Approach: Decide the steps needed. In our exercise, first convert to a decimal, then to a percent, and finally round.
• Execute the Steps: Work through each part methodically. Use calculations carefully for accuracy.
• Review Your Solution: Double-check each step and the final answer. Ensure it matches the question's requirements.

These strategies help maintain clarity and accuracy, cut down errors, and improve confidence in tackling various math problems.