Problem 24 - Prealgebra

Question

Change each decimal to a percent. $$0.87$$

Step-by-Step Solution

Answer

0.87 as a percent is 87%.

Step 1: Understand the concept

To convert a decimal to a percent, you need to understand that 'percent' means 'per hundred'. Therefore, converting a decimal to a percent involves shifting the decimal point two places to the right.

Step 2: Shift the Decimal Point

Take the given decimal, 0.87, and move the decimal point two places to the right. This converts 0.87 into 87.

Step 3: Add the Percent Symbol

After moving the decimal point in 0.87 to get 87, simply add the percent symbol (%) to express it as a percentage. So, 0.87 becomes 87%.

Key Concepts

Understanding Percentages

Percentages are a way of expressing a number as a fraction of 100. When we say 87%, we mean 87 per 100. This system makes it easy to compare values. For instance, if you scored 87% on a test, it means you got 87 out of every 100 available points.

• One key advantage of percentages is their universal applicability, making them useful in various contexts like finance, statistics, and everyday life.
• They help us understand proportions easily. For example, if you see that 50% of a pie has been eaten, you know instantly that half is gone.

Percentages are often used to describe increases and decreases. For instance, if something has increased by 10%, it means it is now 10% higher than it was originally.

Decimal to Percent Conversion

Converting decimals to percentages is straightforward once you grasp the concept that 'percent' means 'out of 100'. Whenever you have a decimal, like 0.87, the conversion process involves moving the decimal point two places to the right. For instance, with 0.87:

• Moving the decimal two spots right turns 0.87 into 87.
• The last step is to add a percent sign resulting in 87%.

This transformation works because decimals are based on units of one, whereas percentages are based on units of 100. By shifting the decimal, you align it with the concept of 'per hundred', which gives you the percentage.

Basic Math Concepts

Understanding basic math concepts is essential for tackling things like decimal to percent conversion. Numbers can be expressed in various forms, including fractions, decimals, and percentages, each form serving a different purpose in helping us calculate and compare values.

• Decimals are fractions expressed in base ten, making them perfect for calculations where precision is necessary.
• Fractions indicate portions of a whole, showing relationships between parts of an object or set.
• Percentages simplify comparing scales because they break down values into a standard 'per 100' format.

By mastering these basic math concepts, students can easily convert between different numerical representations and gain a deeper understanding of quantities and their relationships in everyday situations.