What is 20 percent of 240

Step-by-step calculation

To find 20 percent of 240, we follow a simple calculation process.

Step 1: Identify the values:

• Total Value (Whole): $240$
• Percentage: $20\%$

Step 2: Convert the percentage to a decimal:

Step 3: Multiply the total value by the decimal:

Step 4: Perform the multiplication:

Therefore, 20 percent of 240 is 48.

Explanation of Percentage Calculation

Percentage calculation is a mathematical technique used to determine the proportion of a part to a whole, expressed as a fraction of 100. It is a crucial concept in various fields such as finance, statistics, and general arithmetic.

Basic Formula

The general formula for calculating a percentage is:

Where:

• Part is the portion of the whole you are interested in.
• Whole is the total amount or quantity.

Example Calculation

Consider you have 20 apples out of a total of 50 apples. To find the percentage of apples you have, you would use the formula as follows:

So, you have 40% of the total apples.

Common Uses

1. Marks and Grades: Calculating academic performance.
2. Financial Analysis: Determining interest rates, profit margins, and ratios.
3. Statistics: Representing data, such as population percentages.

Conversion to and from Percentages

• To convert a decimal to a percentage: Multiply by 100.

  For instance, $0.75 \times 100 = 75\%$.

• To convert a fraction to a percentage: First, convert the fraction to a decimal, then multiply by 100.

  For example, $\frac{3}{4} = 0.75$, and then $0.75 \times 100 = 75\%$.

Real-Life Application

Let’s say you got 85 marks out of 100 in a test. To find the percentage:

Hence, you scored 85% on your test.

Summary

Understanding how to calculate percentages helps in interpreting and comparing different quantities. Whether it's grades, financial data, or statistical information, percentages provide a clear and standardized way to represent parts of a whole.

Explanation of Decimal Conversion

Decimal conversion is the process of converting a number from one base to another. This is particularly useful in various fields such as computer science, mathematics, and engineering. The most common conversions involve:

• Decimal to binary
• Decimal to hexadecimal
• Decimal to octal

Converting Decimal to Binary

Binary is base-2, which means it uses only 0 and 1. To convert a decimal number to binary, you repeatedly divide the number by 2 and write down the remainder. The binary number is the series of remainders read from the bottom up.

Example: Convert 13 to binary

1. $13 \div 2 = 6$ remainder $1$
2. $6 \div 2 = 3$ remainder $0$
3. $3 \div 2 = 1$ remainder $1$
4. $1 \div 2 = 0$ remainder $1$

Reading from bottom to top, $13$ in binary is $1101$.

Converting Decimal to Hexadecimal

Hexadecimal is base-16, using digits 0-9 and letters A-F. The conversion process is similar to binary but divides by 16 instead of 2.

Example: Convert 254 to hexadecimal

1. $254 \div 16 = 15$ remainder $14$

Since 14 in hexadecimal is 'E', $254$ in hexadecimal is $FE$.

Converting Decimal to Octal

Octal is base-8, so it uses digits 0-7. The conversion is done by repeatedly dividing by 8.

Example: Convert 83 to octal

1. $83 \div 8 = 10$ remainder $3$
2. $10 \div 8 = 1$ remainder $2$

So, $83$ in octal is $123$.

Mathematical Representation

For a more formal approach, the conversion from decimal $D$ to any base $b$ can be represented as:

where $d$ are the digits in the new base.

For example, converting a decimal number $46$ to base $3$:

Thus, $46$ in base 3 is $1211_3$.

Important Points

• Understanding positional value: Each digit represents a power of the base.
• Repeated division/remainder method: A practical way to handle conversions manually.
• Calculator tools and algorithms: Useful for handling large numbers or automated conversions.

This fundamental concept is crucial for various applications, especially in computing, where binary and hexadecimal systems are prevalent.