Problem 77 - 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. $$\frac{6}{51}$$

Step-by-Step Solution

Answer

11.8%

Step 1: Convert Fraction to Decimal

To convert the fraction \( \frac{6}{51} \) into a decimal, divide 6 by 51. Using a calculator, perform the division: \( 6 \div 51 \approx 0.117647 \).

Step 2: Convert Decimal to Percentage

To convert the decimal 0.117647 to a percentage, multiply by 100. So, \( 0.117647 \times 100 = 11.7647 \).

Step 3: Round to the Nearest Tenth of a Percent

To round 11.7647 to the nearest tenth of a percent, look at the hundredths digit, which is 6. Since 6 is 5 or higher, round up the tenths place from 7 to 8, resulting in 11.8%.

Key Concepts

Percent Conversion

Percent conversion is a method used to change a decimal number into a percentage. This is particularly useful in various fields like finance and statistics, as it provides a clearer view of relative data. To convert a decimal to a percent, you multiply the decimal by 100. Consider a decimal such as 0.117647. To convert this into a percentage:

• Multiply the decimal by 100: \( 0.117647 \times 100 = 11.7647 \).
• Now, you have the decimal expressed as a percentage: 11.7647%.

This allows anyone interpreting the number to immediately understand it as a proportion of 100, making it more relatable and easier to understand in practical comparisons.

Decimal Rounding

Decimal rounding is a mathematical process of reducing the digits of a number while keeping its value close to the original. When expressing percentages, rounding helps simplify and make numbers more understandable. To round to the nearest tenth, follow these simple steps:

• Identify the digit in the tenths place.
• Look at the digit immediately after it - this is the hundredths digit.
• If the hundredths digit is 5 or greater, increase the tenths digit by 1. Otherwise, leave the tenths digit unchanged.
  For example, to round 11.7647 to the nearest tenth, notice the tenths digit is 7 and the hundredths digit is 6. Since 6 is greater than 5, you round up, adjusting 7 to 8. Thus, the rounded number is 11.8%.

This practice ensures numbers are concise yet adequately represent the original values.

Calculator Usage

Calculators are essential tools in both academic and practical math applications. Understanding how to effectively utilize a calculator can greatly enhance your mathematical accuracy and speed.Here is how to use a calculator for fraction to decimal conversion:

• Enter the numerator (the top number of the fraction).
• Press the division key.
• Enter the denominator (the bottom number of the fraction).
• Press the equals key to get your decimal result.

In the example of converting \( \frac{6}{51} \):

• Input: 6, press divide, then input: 51, and press equals.
• Resulting in a decimal: 0.117647.

With practice, using a calculator becomes second nature, aiding in precise calculations and conversions.