Problem 58 - Elementary Algebra

Question

For exercises \(47-58\), rewrite the percent as a decimal number. $$ 0.3 \% $$

Step-by-Step Solution

Answer

0.003

Step 1 - Understand the Percent

A percent represents a number out of 100. In this exercise, we need to convert the given percent into a decimal.

Step 2 - Divide by 100

To convert a percent to a decimal, divide by 100. Here, take the percent value, which is 0.3, and divide by 100: \[ 0.3 \div 100 \]

Step 3 - Perform the Division

Now, perform the division: \[0.3 \div 100 = 0.003\]

Key Concepts

Percent

A percent is a way to express a number as a part of a whole, specifically out of 100. The word 'percent' comes from Latin 'per centum', meaning 'by the hundred'. When you see a percentage, like 0.3%, it tells you how many parts out of 100 you have. So, 0.3% means 0.3 out of 100.
Understanding this is a crucial step before you can convert a percentage into another form, like a decimal. It helps us make meaningful comparisons and measurements in everyday life.
In our example, we had 0.3%. This tells us we have 0.3 parts out of each 100 parts.

Decimal Conversion

To convert a percent to a decimal, the main operation involves dividing by 100. Think about what percent means: 'per 100'. This means you're essentially shifting the decimal point two places to the left.
Here’s a small guide to help you remember:

• Move the decimal point two places to the left
• Remove the percent symbol

So, if you have 0.3%, start by identifying the decimal point in the number. For 0.3, the decimal point is just after the 0. Now, move that decimal point two places to the left.
Before:
0.3%
During conversion:
0.003
Lastly, remove the percent symbol to get the final decimal value:
0.003

Division

Division is one of the basic mathematical operations that is vital for the decimal conversion of percentages. In our process, we're dividing the percentage value by 100.
To visualize this, take the number from the percentage: 0.3. Now, set up a division problem where 0.3 is divided by 100.
This can be written as:
\[0.3 \div 100 = 0.003\]
To divide a number by 100, you are essentially moving the decimal place two positions to the left. This is a universal rule and works for any percentage:

• 0.3 ÷ 100 = 0.003
• 50 ÷ 100 = 0.5
• 25 ÷ 100 = 0.25

Understanding division helps break down complex operations into simpler steps, making the process straightforward.