Problem 13 - Prealgebra

Question

Change each percent to a decimal. $$9 \%$$

Step-by-Step Solution

Answer

9% as a decimal is 0.09.

Step 1: Understanding Percents

Percent means per hundred, so 9% means 9 out of 100.

Step 2: Converting Percent to Decimal

To convert a percentage to a decimal, remove the percent sign and divide by 100. This means we take 9% and divide 9 by 100.

Step 3: Performing the Division

Divide 9 by 100 to get the decimal form. This gives us 0.09.

Key Concepts

Percent to Decimal Conversion

Converting percentages to decimals is an essential arithmetic skill. It becomes incredibly handy in various areas like finance, data analysis, and everyday calculations. The main idea is straightforward: you need to change a percentage into its decimal form.

Here's how you can easily do it:

• Firstly, remove the percent sign (\(\%\)).
• Then, divide the number by 100. This is equivalent to moving the decimal point two places to the left.

For example, changing 9\(\%\) to a decimal involves shifting the decimal point left as though you are dividing by 100. The result is 0.09. This simple conversion shows how percentages fit within the decimal system, making percentages easier to handle in calculations!

Basic Arithmetic

Basic arithmetic is the branch of mathematics that deals with the basic operations of numbers: addition, subtraction, multiplication, and division. These operations are foundational skills necessary for solving all sorts of mathematical problems.

A crucial part of converting percentages to decimals involves the basic arithmetic operation of division. When you change a percentage to a decimal, you divide by 100. Why 100? Because percent means per hundred, so you're literally calculating how many hundreds make up the percentage.

Performing the division of a small number like 9 by 100 involves shifting the digits to fit into a smaller space or value. Hence, 9 divided by 100 places the decimal point to form 0.09, which is much smaller than the original number.

Understanding Percents

Understanding percents is about understanding how they relate to the whole. The word "percent" comes from the Latin 'per centum', meaning "by the hundred." This means when you are talking about percent, you are considering something out of 100.

For example, 9\(\%\) literally means 9 out of 100. It's important to grasp this concept because it allows you to see how a part relates to a whole.

Once you understand that percent is a fraction or part of a total, translating this concept into a decimal becomes much more intuitive. Anytime you convert a percentage to a decimal, you simplify that "out of 100" understanding into a form that’s easier to calculate and use in equations. This fundamental understanding bridges percentages with both fractions and decimals, making calculations more efficient.