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Chapter 6: Problem 9

Find \(30 \%\) of 1,600

Short Answer

Expert verified
Therefore, \(30%\) of 1,600 is 480.

Step by step solution

01

Convert Percentage to Decimal

To convert a percentage to a decimal, divide the percentage value by 100. Therefore, the decimal value for 30% is \(30 \div 100 = 0.30\).
02

Multiply by the Given Number

Multiply the decimal obtained in the previous step (0.30) by the given number (1,600). Therefore, the calculation is \(1600 \times 0.30 = 480\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding How to Convert Percentages to Decimals
To solve problems involving percentages, it's essential to first convert percentages into decimals. This is because mathematical operations are easier with decimals. The process is quite simple: divide the percentage value by 100. This division converts the percentage to a decimal. For example, if you have 30%, you convert it as follows:
  • 30% is divided by 100, which equals 0.30.
This is the decimal form of 30%. Essentially, you're moving the decimal point two places to the left. This small step is vital for performing further calculations accurately. Remember, without converting percentages to decimals, subsequent arithmetic operations may not yield correct results.
Mastering the Art of Multiplying Decimals
Once a percentage is converted to a decimal, calculations often involve multiplying this decimal by another number. This process is straightforward if you follow these steps:
  • Write down the numbers aligning them by their rightmost digits. Decimal points should be ignored for the moment.
  • Multiply as if working with whole numbers.
  • Count the total number of decimal places in both numbers.
  • Place the decimal point in the product, ensuring the same number of decimal places as counted in the previous step.
For instance, to find 30% of 1,600, you multiply 0.30 by 1,600. Following the steps:
  • Ignore the decimals for now, treat it as 30 x 1600 = 48,000.
  • The decimal 0.30 has two decimal places, so the result must reflect this.
  • Thus, adjust by placing the decimal: 480.00.
This results in a final product of 480.
The Role of Basic Arithmetic Operations in Problem Solving
Basic arithmetic operations鈥攁ddition, subtraction, multiplication, and division鈥攁re the foundation of more complex calculations, including those involving percentages and decimals. They are straightforward, yet knowing them well brings clarity and ease to solving mathematical problems.
  • Division in percentage conversion is essential: dividing by 100 transforms percentages to a usable form.
  • Multiplication comes into play when finding a portion of a number, such as finding 30% of 1,600.
Understanding the sequence of these operations is crucial. In many scenarios, like the one considered here, you convert the relevant numbers and then apply multiplication to obtain your answer. Keeping operations orderly ensures success in reaching the correct outcome.

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