Problem 76 - Prealgebra

Question

Use a calculator to write each fraction as a decimal, and then change the decimal to a percent. Round all answers to the nearest tenth of a percent. $$\frac{18}{83}$$

Step-by-Step Solution

Answer

\( \frac{18}{83} \approx 21.7\% \)

Step 1: Convert the Fraction to a Decimal

To convert the fraction \( \frac{18}{83} \) into a decimal, divide 18 by 83 using a calculator. The result is approximately 0.216867.

Step 2: Convert the Decimal to a Percent

To convert the decimal 0.216867 to a percent, multiply it by 100. The computation is 0.216867 \( \times \) 100 = 21.6867.

Step 3: Round to the Nearest Tenth of a Percent

Round the number 21.6867 to the nearest tenth of a percent. Look at the hundredths place, which is 8, and since it is 5 or more, round up. Thus, 21.6867 becomes 21.7.

Key Concepts

Rounding Decimals

When working with decimal numbers, it's often necessary to round them to make the numbers easier to understand and use, especially in real-life applications. Rounding means adjusting the number to the nearest specified place value.
To round a decimal to the nearest tenth, follow these simple steps:

• Identify the digit in the tenths place. This is the first digit to the right of the decimal point.
• Look at the digit in the place right after the tenths place, which is the hundredths place.


• If the hundredths digit is 5 or more, increase the tenths digit by one.
• If the hundredths digit is less than 5, leave the tenths digit unchanged and remove the rest.

In our example, the decimal 21.6867 becomes 21.7 because the hundredths digit is an 8, which means the tenths digit should be rounded up. This process helps simplify numbers, making them easier to read and use in practical situations.

Decimals to Percents

Converting decimals to percents is a straightforward process that involves multiplying the decimal number by 100. This transformation helps turn the decimal into a more familiar and easy-to-interpret format — the percent.
Here’s how you can do it:

• Take your decimal number, such as 0.216867.
• Multiply it by 100 to turn it into a percent. This simply shifts the decimal point two places to the right.

Thus, in our example, 0.216867 becomes 21.6867 percent after multiplication. Converting decimals to percents is exceptionally useful in various applications, such as calculating discounts, statistics, and interest rates. As you become familiar with this process, you will find it easier to interpret decimals and percents interchangeably.

Using Calculators for Math

Calculators are incredibly useful tools when working with fractions, especially when you need to convert them into decimals and then into percents. They provide accurate and quick results, which are essential for precise calculations.
Here’s a simple guide on using calculators effectively in such conversions:

• Input the numerator of the fraction and then divide by the denominator. For instance, input 18 ÷ 83 to get 0.216867.
• Use the function to multiply your decimal result by 100 if your goal is to convert to a percent. Simply input 0.216867 × 100 to get 21.6867.

Once you have performed these calculations, using the calculator's rounding function (if available) can speed up your work by rounding numbers as specified. Using a calculator ensures you can handle more complex numbers with ease and focus on understanding the steps without worrying about arithmetic errors.