Problem 17 - Intermediate Algebra

Question

A. Write \(2.5 \%\) as a decimal. B. Write 0.06 as a percent.

Step-by-Step Solution

Answer

A: 0.025, B: 6%

Step 1: Understand Percentages

Percentages can be converted to decimals by dividing the percentage by 100.

Step 2: Convert Percentage to Decimal

For part A, convert \(2.5\%\) to a decimal by dividing by 100. Calculate this as follows: \(2.5\div 100 = 0.025\).

Step 3: Reverse the Process for Decimal to Percent

Decimals can be converted to percentages by multiplying the decimal by 100.

Step 4: Convert Decimal to Percentage

For part B, convert 0.06 to a percentage by multiplying by 100. Calculate this as follows: \(0.06 \times 100 = 6\%\).

Key Concepts

decimal to percent conversion

When you're looking to convert decimals into percentages, there’s a really easy trick. All you've got to do is multiply the decimal number by 100. Think of it this way: percentages are simply decimals that have been scaled up by a factor of 100 to make them easier to understand. Let’s break this down a bit more.

• Start with your decimal number. For instance, if you have 0.06, that’s your starting point.
• Multiply it by 100. That means you take that decimal and move it two places to the right. With 0.06, this gives you 6. In this case, it transforms 0.06 into 6%.

This technique works because you’re effectively showing how much of 100 parts the decimal represents. It’s like saying 0.06 of a complete unit is equivalent to 6 out of 100 parts.

basic algebra

In basic algebra, understanding percentages and their conversion to decimals is just one of the many fundamental skills. Algebra often deals with numbers in different forms, and it is essential to be comfortable switching between these forms. Let's explore the essence:

• Algebra teaches us to manipulate numbers and symbols. So, knowing how to convert percentages to decimals and vice versa is a core skill.
• For example, if you have an equation that includes 0.06, you should be able to read it as a percentage, which is 6%.
• This skill is useful when solving equations that involve increase or decrease, often represented in percentages.

The concepts of multiplication and division are directly applied here. For instance, to shift between percentages and decimals, you multiply or divide by 100. This mirrors many operations in algebra where you adjust numbers to solve equations. By mastering this, algebra becomes a more intuitive and powerful tool.

percentages

Percentages play a huge role in everyday life, and understanding them is crucial. They are all about parts per hundred, so they make it simple to understand proportions and comparisons during calculations. Let’s examine percentages more closely:

• A percentage is a number or ratio expressed as a fraction of 100. For example, if you see 50%, it means 50 out of 100.
• Understanding percentages is vital in settings like shopping discounts, interest rates, and statistics. It helps to assess and compare different quantities directly.
• You’ll often need to convert numbers: for instance, translating 2.5% into a decimal gives you 0.025, which can be easily understood in algebraic operations or financial calculations.

The great thing about percentages is that they present a universal way to compare any number of items, regardless of total size. Whether you’re dealing with money, scores, or any other form of data, percentages simplify the comparison process by breaking it down into a common scale.