Problem 61 - Prealgebra

Question

Write as a percent. $$0.07$$

Step-by-Step Solution

Answer

0.07 as a percent is 7%.

Step 1: Understand the Concept

To convert a decimal into a percentage, we multiply the decimal number by 100. This is because 'percent' means 'per hundred'. Therefore, every whole number is multiplied by 100 to establish its percentage form.

Step 2: Perform the Conversion

Take the given decimal number, which is 0.07, and multiply it by 100. This means you calculate \(0.07 \times 100\).

Step 3: Calculate the Multiplication

When you multiply 0.07 by 100, it shifts the decimal point two places to the right, resulting in the number 7. Therefore, \(0.07 \times 100 = 7\).

Step 4: Express as a Percentage

The result from step 3 gives us the percentage form. Therefore, 0.07 expressed as a percentage is 7%. This means that 0.07 is equivalent to 7%.

Key Concepts

Converting Decimals to Percents

Understanding how to convert decimals into percents is a fundamental math skill that can help you in many areas of everyday life, from financial literacy to data interpretation. The basic premise is simple: to convert any decimal to a percent, you multiply it by 100.
Think of the word "percent" as "per hundred." This means that when you convert a decimal to a percent, you are essentially finding out how much that decimal is out of 100.
For example, when converting the decimal 0.07 to a percent, you multiply it by 100. This moves the decimal point two places to the right, turning 0.07 into 7. Thus, 0.07 expressed as a percent is 7%.

• Simply multiply the decimal by 100.
• Move the decimal two spaces to the right.
• Add the percentage sign (%) to indicate the value is a percent.

This simple method is always applicable for direct conversion from decimals to percents.

Multiplying Decimals

Multiplying decimals isn’t as scary as it seems, and it’s a helpful skill that you'll use in converting decimals to percentages, among other applications.
When you multiply decimals, just follow these steps: multiply as you would with whole numbers, then take care of the decimal point placement in the final answer.
For our example of converting 0.07 to a percent, we did the multiplication 0.07 × 100, which essentially moves the decimal point two places to the right. Here’s a cheat sheet to remember:

• Ignore the decimal points initially and multiply the numbers as if they're whole numbers.
• Count the total number of decimal places in the factors.
• Place the decimal point in the result so that it has the same number of decimal places.
• In this specific conversion, multiplying by 100 means moving the decimal point, making it easier.

The magic of multiplying decimals mainly lies in remembering where to place the decimal point in your final answer.

Expressing Decimals as Percentages

Expressing decimals as percentages is a straightforward task once you grasp the basic process of decimal multiplication and conversion. The percentage format is prevalent in various real-world applications, hence mastering it can be tremendously beneficial.
Here's the quick method we follow:
1. Multiply the given decimal by 100. 2. Move the decimal two places to the right. 3. Add a percent sign (%) to symbolically express the result.
When you start with 0.07 and follow these instructions, it converts to 7%, which represents 7 "per hundred". This reveals what fraction or part of a hundred the given decimal equates to.
The conversion process is a quick mental calculation that becomes even easier with practice. Remember:

• The multiplier of 100 is key: it transforms the decimal into a percentage effectively.
• By adjusting the decimal point to the right by two places, you align it with its "per hundred" equivalent.
• The percentage symbol marks your final result as a part of a whole, represented by 100 units.