More details please. Why did we convert 48 percent to a decimal

To provide more detail, let's explore why we converted 48% to a decimal and how that affects our calculations.

### Understanding Percentages and Decimals

A **percentage** represents a fraction out of 100. The word "percent" literally means "per hundred." So, when we say 48%, we mean 48 out of every 100. Mathematically, percentages are often more conveniently expressed as **decimals** for calculation purposes.

To convert a percentage to a decimal, you divide the percentage by 100. For example:

\[
48\% = \frac{48}{100} = 0.48
\]

### Why Convert to a Decimal?

Converting to a decimal simplifies the arithmetic when working with percentages in equations. Using decimals allows us to multiply directly, which is typically easier than working with percentages as fractions or ratios. 

### Step-by-Step Solution with Decimals

1. **Set up the equation**:
   - We know that 300 macarons represent 48% of the total number of macarons, denoted as \( T \).

2. **Convert the percentage to a decimal**:
   - 48% is converted to a decimal by dividing by 100:  
   \[
   48\% = 0.48
   \]

3. **Formulate the equation**:
   - Since 300 is 48% of \( T \), we write:  
   \[
   300 = 0.48 \times T
   \]

4. **Solve for \( T \)**:
   - To find the total \( T \), divide both sides by 0.48:  
   \[
   T = \frac{300}{0.48}
   \]

5. **Calculate \( T \)**:
   - Now perform the division:  
   \[
   T = \frac{300}{0.48} = 625
   \]

So, \( T = 625 \). This means the total number of macarons sold was **625**.

### Summary

- **Why convert to a decimal?**: It simplifies multiplication and division in calculations involving percentages.
- **How did it help here?**: By converting 48% to 0.48, we could directly multiply and divide to find the total \( T \).

Would you like further clarification, or do you have any questions?

### 5 Related Questions

1. How do you convert other percentages, like 25% or 75%, to decimals, and why is it useful?
2. If 48% equals 300 macarons, what is the total when 36% equals 270 macarons?
3. How would you calculate the total if you knew 300 macarons represented 30% of the total?
4. What is the formula for finding the percentage of a part of a total?
5. Can you demonstrate how to solve a similar problem using a fraction instead of a decimal?

**Tip:** When dealing with word problems involving percentages, it's always helpful to clearly define what each number represents and write down what you're solving for.

Learn how to convert 48% to a decimal and understand its significance in calculations. This problem explores basic arithmetic concepts, focusing on percentages and decimals. Suitable for students in Grades 6-8.

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