Problem 24 - Basic Engineering Mathematics

Question

Express as percentages: (a) \(1.875\) and (b) \(0.0125\)

Step-by-Step Solution

Answer

(a) 187.5%, (b) 1.25%

Step 1: Convert the Decimal for Part (a) into a Percentage

To convert a decimal into a percentage, multiply the decimal number by 100. For part (a), we have the decimal \(1.875\). Thus, the calculation is: \(1.875 \times 100\).

Step 2: Simplify the Calculation for Part (a)

Perform the multiplication: \(1.875 \times 100 = 187.5\). This means \(1.875\) as a percentage is \(187.5\%\).

Step 3: Convert the Decimal for Part (b) into a Percentage

For part (b), take the decimal \(0.0125\) and multiply by 100. This gives us: \(0.0125 \times 100\).

Step 4: Simplify the Calculation for Part (b)

Carry out the multiplication: \(0.0125 \times 100 = 1.25\). Hence, \(0.0125\) as a percentage is \(1.25\%\).

Key Concepts

Decimals to Percentages

Converting decimals to percentages is a fundamental concept in mathematics, often used to make numbers easier to interpret. A percentage expresses a number as a part of one hundred, so to convert a decimal into a percentage, you multiply by 100.

For example, to convert the decimal \(1.875\) into a percentage, you multiply \(1.875\) by 100, resulting in \(187.5\%\). Similarly, for a smaller decimal like \(0.0125\), multiplying by 100 yields \(1.25\%\).

This process is straightforward:

• Move the decimal point two places to the right.
• Add the percentage sign \(\%\).

This conversion is useful in many real-world scenarios, such as calculating interest rates, growth percentages, and discounts.

Mathematical Operations

Understanding how basic mathematical operations work is essential for performing accurate calculations.The primary operation involved in percentage conversion is multiplication. When converting a decimal to a percentage, you use multiplication as follows:

• Identify the decimal number.
• Multiply the decimal by 100.

For instance, in the conversion of \(1.875\) to \(187.5\%\), the multiplication operation \(1.875 \times 100\) is executed.

This type of multiplication is a simple arithmetic operation, but it's important to ensure all multiplication is computed correctly, using methods such as:

• Stacked multiplication for manual calculations.
• Utilizing calculators for quick computation.

Understanding multiplication in this context will help solidify your grasp on transforming numbers in various forms.

Step-by-Step Calculations

Solving problems with a clear, step-by-step approach is beneficial in understanding the entire process of conversions and operations.

For our exercise, follow these steps: 1. **For a decimal like \(1.875\):** - Multiply by 100: \(1.875 \times 100 = 187.5\) - So, \(1.875\) becomes \(187.5\%\).2. **For a smaller decimal such as \(0.0125\):** - Multiply by 100: \(0.0125 \times 100 = 1.25\) - Thus, \(0.0125\) turns into \(1.25\%\).This procedure demonstrates the concrete steps needed for converting decimals, reinforcing the mathematical operations required. Following this clear process ensures you don't miss any crucial steps during conversions or other mathematical tasks. The outlined method can be applied universally for decimal to percentage conversions.