Problem 80 - 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. $$\frac{568}{732}$$

Step-by-Step Solution

Answer

77.6%

Step 1: Convert Fraction to Decimal

Use a calculator to divide the numerator by the denominator: \( 568 \div 732 \). This gives a decimal value of approximately \( 0.775956938 \).

Step 2: Convert Decimal to Percent

To convert a decimal to a percent, multiply the decimal by 100. Therefore, \( 0.775956938 \times 100 = 77.5956938 \).

Step 3: Round to the Nearest Tenth

Round the percent from the previous step to the nearest tenth. Since the number is \( 77.5956938 \), rounding to the nearest tenth gives \( 77.6\% \).

Key Concepts

Converting Decimals to Percents

Changing a decimal to a percent is a straightforward process. This conversion helps us express a part of a whole in terms of 100. For example, if you have a decimal of 0.775, it can be turned into a percentage by:

• Multiplying the decimal by 100.
  • For example, with 0.775, you calculate: 0.775 × 100 = 77.5.
• Adding the percent symbol (%) to the result.

This gives us a value of 77.5%. When you look at it as a fraction of 100, it is much easier to understand the proportion. It signifies that 77.5 parts out of every 100 are in relation to the whole.

Using a Calculator

Calculators are invaluable tools when it comes to converting fractions to decimals quickly and accurately. To change a fraction like \( \frac{568}{732} \) to a decimal:

• Enter the numerator (568) first.
• Press the divide symbol (÷ or /).
• Enter the denominator (732) next.
• Press the equal sign (=) to get the decimal result.

This will give you a decimal number that can be further used in calculations. It’s always a good practice to check your calculator’s mode and ensure you have entered everything correctly to avoid errors.

Rounding to the Nearest Tenth

Rounding numbers helps simplify them by reducing the number of decimal places. When you round to the nearest tenth, you focus on the first digit after the decimal point. For example, if you have the number 77.5956938 and need to round it to the nearest tenth:

• Look at the number in the hundredths place, which is 9 in this case.
• If this digit is 5 or greater, increase the tenths place by one. Here, the tenths place (7) increases to 8.
  • Giving you a final rounded value of 77.6.
• If it were less than 5, the tenths place would stay the same.

Rounding ensures numbers are easy to communicate and understand, particularly in reports and everyday calculations. It is a key skill when dealing with percentages and other numerical data.