Problem 39 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth,if necessary. $$2.7$$

Step-by-Step Solution

Answer

2.7 is 270% when expressed as a percent.

Step 1: Understanding Percent Conversion

To convert a decimal to a percent, we need to multiply the decimal by 100. This is because the word percent means 'per hundred.' So, multiplying the decimal number by 100 will give us the equivalent value in percent form.

Step 2: Convert 2.7 to a Percent

Now, we'll multiply 2.7 by 100 to convert it to a percent. \[ 2.7 \times 100 = 270 \]

Step 3: Final Result

The result of our calculation is 270. Since there is no need to round, we can directly express the answer. Thus, 2.7 expressed as a percent is 270%.

Key Concepts

Converting Decimals to Percent

To convert decimals into a percentage, the key step is to multiply the decimal number by 100. This transformation is due to the definition of "percent," which translates to "per hundred." When converting a decimal like 2.7 into a percent, you perform the following multiplication:

• Take the decimal number, in this case, 2.7.
• Multiply by 100: \(2.7 \times 100 = 270\).

This will give you the decimal expressed as a percentage. It's a straightforward process that turns any decimal figure into an easily understandable percent format. Remember, every time you're presented with a decimal, the conversion rule stays the same.

Rounding in Percentage Conversion

Rounding can often be necessary when converting decimals to percentages, especially when dealing with decimals that result in non-whole number percentages. While converting 2.7 to percent resulted in 270%, rounding wasn’t needed here. But imagine converting something like 2.756. In such cases, after multiplying by 100, you'd end up with 275.6%, which you might need to round to a nearby whole or tenths place, depending on your requirement. Here are the steps to round:

• Check the digit immediately after your desired decimal place. For the tenth, check the hundredth digit.
• If the digit is five or greater, round up.
• If less than five, round down.

Rounding helps to simplify figures and make them more manageable in calculations or presentations.

The Role of Multiplication in Percentages

Multiplication is crucial when converting decimals to percentages. This step takes the decimal figure and effectively "moves" it two places to the right on the number line. Let's break down why and how this happens.

• The essence of percentage is the idea of a part out of one hundred.
• By multiplying by 100, each part of the decimal is scaled up to relate to 100 parts.
• This action is what gives us the "percent" value, making it readable and useful in everyday contexts.

This multiplication not only transforms the initial number but also facilitates easier comparisons and comprehensions across different numeric contexts.

Understanding the Percent Concept

The concept of percent is fundamental in mathematics, yet it also pops up in our daily lives often—think about sales, interest rates, or statistics. Here's a simplified breakdown:

• "Percent" comes from the Latin "per centum," meaning "by the hundred."
• It is a way to express a number as a fraction of 100, hence making comparisons easier.
• In mathematics, percentages represent a portion of a whole, facilitating understanding and communicating proportions.

Understanding percent expands one's ability to engage with everyday calculations, from determining discounts to understanding data analysis.