Problem 1 - Technical Mathematics with Calculus

Question

Convert each decimal to a percent. $$3.72$$

Step-by-Step Solution

Answer

3.72 as a percent is 372%.

Step 1: Understanding Percent Conversion

Converting a decimal to a percent involves shifting the decimal point two places to the right. This is equivalent to multiplying the decimal by 100.

Step 2: Apply the Percent Conversion

Multiply the decimal number 3.72 by 100 to convert it to a percent. This is done by moving the decimal point two places to the right.

Step 3: Express as a Percent

After moving the decimal point two places to the right, append the percent sign (%) to the number to express it as a percent. So, 3.72 becomes 372%.

Key Concepts

Percent Conversion

When we talk about converting decimals to percents, we are essentially discussing how to express a number as a fraction of 100. This is a fundamental concept in understanding percentages. To convert a decimal to a percentage, you multiply the decimal by 100. This action shifts the decimal point two places to the right. For example, if we have the decimal 0.57, moving the decimal point two places to the right gives us 57, and we simply add a percent sign to express it as a percentage, resulting in 57%.

This method of conversion is necessary in many real-world contexts, such as calculating discounts, interest rates, and statistical data, where understanding the percentage can make information more relatable and easier to comprehend. A handy trick to remember is that 'cent' in 'percent' signals the relation to 100, as in a century or a centimeter, which imply one hundred years and one hundredth of a meter, respectively.

Decimal Multiplication

Understanding decimal multiplication is crucial when converting decimals to percentages. In essence, when you multiply a decimal by 100, you are doing two things: shifting the decimal point two places to the right and transforming the value into a whole number equivalent to its percentage form. Multiplying by 100 may seem daunting, but it's actually quite straightforward once you know the trick of the shifting decimal point.

Using the example of the decimal 3.72, imagine the decimal point as being flexible, moving two spots to the right when multiplying by 100. The first move changes 3.72 to 372.0, and the second move drops the trailing zero to finalize 372. This simple step eliminates the need for complex arithmetic and clearly demonstrates the intended percentage as 372%.

Mathematical Notation

Mathematical notation is the shorthand of math; it's the system of symbols and numbers used to represent quantities and operations. Comprehending mathematical notation is vital for effectively communicating and working with mathematical concepts like decimal to percent conversion. In our example, 3.72 is written in decimal notation, where the number to the left of the decimal point represents whole units, and the numbers to the right represent parts of a whole.

When we convert 3.72 to a percentage, we switch to a different notation, where the symbol % is used to express that the number is a percentage. It's important for students to get comfortable with these symbols because they often represent more than just a number; they communicate a relationship or operation. Thus, when we say 3.72 is equivalent to 372%, the % symbol informs us that 372 is a rate per 100, not simply the number 372.