Problem 82 - Algebra A Combined Function

Question

Write each decimal as a percent. $$ 2.15 $$

Step-by-Step Solution

Answer

2.15 as a percent is 215%.

Step 1: Convert the Decimal to a Fraction of 100

To write a decimal as a percent, start by recognizing that a percent is a fraction out of 100. For the decimal 2.15, first think of it as a fraction over 1: \( \frac{2.15}{1} \)

Step 2: Multiply by 100

To convert a fraction to a percent, multiply the fraction by 100. Apply this to the decimal:\[2.15 \times 100 \]

Step 3: Simplify the Product to Percent Format

Compute the multiplication from the previous step:\[ 2.15 \times 100 = 215 \]This result is the decimal expressed as a percentage.

Step 4: Check Your Result

Reread the conversion to ensure it is correct: \(2.15\) is transformed into a percentage by multiplying by 100, resulting in \(215\%\).

Key Concepts

Decimal Multiplication

Decimals can sometimes feel tricky, but when you approach them with simple steps, they become easy to handle. Decimal multiplication comes into play when you want to manipulate a decimal number within certain calculations, as seen when converting decimals to percentages. For example, to convert a decimal to a fraction, you start by thinking of the decimal as being over 1, like turning 2.15 into \( \frac{2.15}{1} \). Here’s a handy step to keep in mind:

• Identify the decimal number you want to multiply; in this case, it's 2.15.
• Recognize that you can multiply this number by another number, such as 100, to achieve your calculations.

This step prepares the foundation for converting decimals into percentages and other forms by performing simple multiplication operations. The goal is to change the scale of the number without altering its inherent value by merely adding or removing decimal places. By becoming familiar with multiplying decimals, you'll find processes like conversion much simpler and more intuitive.

Percent Conversion

Percent conversion is a common mathematical process that involves transforming a number into a percentage. A percentage is essentially a fraction of 100, which makes it easy to compare different quantities, whether they're money, measurements, or statistics. When converting a decimal like 2.15 to a percentage, follow these straightforward steps:

• Understand that converting to a percentage involves multiplying the decimal by 100.
• Perform the multiplication: \( 2.15 \times 100 \).
• The result is 215, meaning 2.15 as a percentage is 215\%.

This conversion gives you a clear understanding of the decimal in terms of per hundred, offering a more relatable measure for comparison. It's crucial to habituate these steps, as percent conversion is frequently used in financial calculations, data analysis, and everyday comparisons. With practice, this method becomes second nature.

Fraction Multiplication

Fraction multiplication is an essential skill in mathematics that ties into converting decimals into percentages. Understanding fraction multiplication helps simplify and manage numbers in fraction form, easing the process of converting them into other formats, such as percentages.

• Start by representing the decimal as a fraction. For instance, 2.15 becomes \( \frac{2.15}{1} \).
• Next, consider multiplying this fraction by another fraction, like \( \frac{100}{1} \), which effectively scales your value by 100.

Multiply the numerators and denominators separately: you have \( 2.15 \times 100 \), where the denominator remains 1, giving \( \frac{215}{1} \).By transforming decimals into fractions and utilizing fraction multiplication, calculations become more structured, and the number manipulations are straightforward. This skill allows mathematical expressions to take different adjustable formats that can be used interchangeably in different types of problems.