Converting a fraction to a decimal and then to a percentage is a straightforward two-step process that helps in comparing values and understanding proportions.
Step 1: Convert the Fraction to a Decimal
To transform a fraction into its decimal equivalent, you simply divide the numerator (the top number) by the denominator (the bottom number).
Example: Converting $\frac{3}{4}$ to a Decimal
Let's convert the fraction $\frac{3}{4}$ to a decimal.
- Identify the numerator: 3
- Identify the denominator: 4
- Perform the division: $3 \div 4 = 0.75$
So, $\frac{3}{4}$ is equivalent to $0.75$ as a decimal.
For more examples and practice, you can explore resources on converting fractions to decimals.
Step 2: Convert the Decimal to a Percentage
Once you have the decimal, converting it into a percentage is also simple. You multiply the decimal by 100. This effectively moves the decimal point two places to the right and adds a percent sign (%).
Example: Converting $0.75$ to a Percentage
Now, let's convert the decimal $0.75$ (from our previous step) to a percentage.
- Take the decimal: $0.75$
- Multiply by 100: $0.75 \times 100 = 75$
- Add the percent sign: $75\%$
Therefore, $0.75$ is equivalent to $75\%$.
To learn more about decimal to percentage conversions, visit educational math platforms.
The Complete Conversion: Fraction to Decimal to Percentage
Combining both steps, here's how the full process looks:
Example: Converting $\frac{1}{2}$
- Fraction to Decimal: Divide the numerator (1) by the denominator (2): $1 \div 2 = 0.5$.
- Decimal to Percentage: Multiply the decimal (0.5) by 100: $0.5 \times 100 = 50$. Add the percent sign: $50\%$.
So, $\frac{1}{2}$ is $0.5$ as a decimal and $50\%$ as a percentage.
Direct Conversion: Fraction to Percentage (Alternative Method)
While the question specifically asks for the two-step process, it's also worth noting that you can convert a fraction directly to a percentage. This involves dividing the numerator by the denominator and then multiplying the result by 100.
Example: Converting $\frac{3}{5}$
- Divide the numerator (3) by the denominator (5): $3 \div 5 = 0.6$
- Multiply the result by 100: $0.6 \times 100 = 60$
- Add the percent sign: $60\%$
Conversion Summary Table
Format | How to Convert | Example ($\frac{3}{4}$) |
---|---|---|
Fraction to Decimal | Divide numerator by denominator | $3 \div 4 = 0.75$ |
Decimal to Percentage | Multiply by 100 | $0.75 \times 100 = 75\%$ |
Fraction to Percentage (Direct) | Divide numerator by denominator, then multiply by 100 | $(3 \div 4) \times 100 = 0.75 \times 100 = 75\%$ |
Why Understanding These Conversions Matters
Being able to convert between fractions, decimals, and percentages is a fundamental mathematical skill with many practical applications.
- Comparing Values: It allows for easy comparison of different quantities presented in various forms. For instance, knowing that $\frac{1}{4}$ is $25\%$ helps understand discounts or proportions.
- Financial Literacy: Understanding percentages is crucial for calculating interest rates, taxes, tips, and discounts.
- Data Interpretation: In statistics and daily news, data is often presented as percentages or decimals, requiring conversion for full comprehension.
- Everyday Life: From cooking recipes to understanding sports statistics, these conversions are implicitly used regularly.