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Chapter 7: Problem 32

What is \(0.41 \%\) of \(291.1 ?\)

Short Answer

Expert verified
0.41% of 291.1 is approximately 1.19.

Step by step solution

01

Convert Percentage to Decimal

To find a percentage of a number, we first convert the percentage into a decimal. We do this by dividing the percentage number by 100. Thus, we have \(0.41\%\) which becomes \(0.0041\).
02

Multiply the Decimal by the Number

Next, we multiply the decimal value by the given number to find the percentage of that number. So, \(0.0041 \times 291.1\).
03

Calculate the Result

Perform the multiplication: \(0.0041 \times 291.1 = 1.19351\).
04

Round the Result

Finally, we round the result to a reasonable decimal place for clarity, usually two decimal places in practical applications: \(1.19\).

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Key Concepts

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

Decimal Conversion
When working with percentages, converting them into decimal form is essential for performing calculations. A percentage represents a fraction of 100, which means that converting it to a decimal involves a simple division process. For example, to convert a percentage like 0.41% into a decimal, you divide by 100. It works like this:
  • Take the percentage value: 0.41%
  • Divide by 100: \(0.41 \div 100 = 0.0041\)
The result, 0.0041, is the decimal form of 0.41%. This conversion is a fundamental step because it allows you to work with percentages in standard mathematical operations. Remember, always move the decimal point two places to the left when converting percentages to decimals.
Multiplication Steps
Once the percentage is converted into a decimal, the next step is to find its value concerning a given number. This involves simple multiplication. Using our decimal conversion from earlier, 0.0041, we now multiply it by the target number, such as 291.1. Here's how it is done:
  • Take the decimal: 0.0041
  • Multiply by the number: \(0.0041 \times 291.1\)
The multiplication yields a result of 1.19351. This step showcases how percentages interact with real-number quantities and provides a precise calculation of what a certain percentage represents in actual figures. The key is to use the exact decimal and not round prematurely to ensure accuracy.
Rounding Numbers
After performing the multiplication, you often need to round the result to a more practicable number of decimal places. Rounding helps in simplifying numbers, making them easier to read and use in subsequent calculations. With our previous result of 1.19351, rounding generally involves:
  • Choosing the decimal place: Typically, two decimal places are used for clarity
  • Inspecting the third decimal: Here it's 3, which means 1.19351 rounds to 1.19
Rounding is crucial because it controls the level of precision in your work. It is especially helpful in everyday tasks where overly precise numbers are unnecessary. Always remember, when rounding, if your number ends in a 5 and beyond, round up the preceding number by one.

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