Problem 56 - Prealgebra

Question

Write as a percent. $$1.15$$

Step-by-Step Solution

Answer

115%

Step 1: Understand the Relationship between Decimals and Percents

Percent means per hundred. To convert a decimal into a percent, multiply the decimal by 100. This is because a percent represents parts per hundred.

Step 2: Multiply the Decimal by 100

Take the decimal 1.15 and multiply it by 100 to convert it to a percent: \(1.15 \times 100 = 115\).

Step 3: Add the Percent Sign

After multiplying, the result needs to be represented as a percentage. So, append the percent sign (%) to the number obtained in the previous step. Therefore, 115 represents 115%.

Key Concepts

Decimals: Understanding the Basics

Decimals are an important mathematical concept often used in everyday life. They represent numbers that are not whole numbers, using a point (.) to separate the whole part of the number from the fractional part. For instance, in the number 1.15, the digit "1" is the whole number part, while the ".15" is the fractional part. Understanding decimals is crucial because they offer precision in calculations, especially in contexts like finance and measurements.

Decimals can be converted into other forms, such as fractions or percentages, depending on the required application. The placement of the decimal point determines the value of each digit, providing a flexible way to express quantities smaller than one or in between whole numbers. When learning about decimals, remember:

• The number of digits after the decimal point indicates the fractional precision.
• Adding zeros after the decimal point doesn’t change the value (e.g., 1.5 is the same as 1.50).
• Moving the decimal point changes the value (e.g., 1.5 is ten times greater than 0.15).

Percentages: A Hundred-Part Expression

Percentages are widely used to represent a part of a whole with the whole being considered as 100 units. The term 'percent' literally means 'per hundred'. Thus, percentages are essentially fractions with a denominator of 100.

The path to converting decimals into percentages involves multiplying the decimal by 100. This multiplication shifts the decimal point two places to the right, converting the fractional part of the decimal into a whole number that represents parts out of one hundred. For example, converting 1.15 into a percentage entails:

• Multiply 1.15 by 100: 1.15 becomes 115.
• This result signifies that 1.15 is equivalent to 115 parts per hundred, or 115%.

Percentages are useful in numerous applications, such as calculating discounts, understanding statistics, and managing financial data. They serve as an accessible way to compare proportions across different contexts.

Mathematics Education: Promoting Understanding

Learning mathematics is foundational for developing problem-solving skills and logical reasoning. However, concepts like decimals and percentages can sometimes be challenging to grasp. Effective mathematics education focuses on fostering a deep understanding rather than rote memorization.
A well-rounded approach might include:

• Utilizing visual aids such as number lines and pie charts to illustrate how decimals and percentages relate to whole numbers.
• Encouraging practical applications, such as using percentages in shopping scenarios to calculate discounts.
• Offering plenty of practice problems to build proficiency and confidence.

Teachers and educational resources should aim to break down complicated ideas into small, digestible parts. By providing clear explanations and using relatable examples, students can build a solid foundation in mathematics that will serve them in various fields of life and work.