Converting Fractions to Decimal Numbers to Percents

Lesson Overview

• Why Are Fractions, Decimals, and Percents Connected?
• Converting Fractions to Decimals
• Converting Decimals to Percents
• Converting Percents to Decimals
• Converting Percents to Fractions
• Converting Fractions to Percents (Using Decimals)
• All Conversions
• Thought-Provoking Practice Questions
• Common Mistakes to Avoid
• Real-World Connection
• Key Takeaway

Imagine you're baking cookies and the recipe says to use 1/4 of a cup of sugar. Then you find another recipe that says 25% sugar. Confused? You're not alone. Understanding how to convert fractions, decimals, and percents helps you compare numbers easily-whether in recipes, sports stats, or discounts at your favorite store. In this lesson, you'll master these conversions step by step, making math useful in everyday life.

Why Are Fractions, Decimals, and Percents Connected?

All three-fractions, decimals, and percents-are different ways to express parts of a whole:

• Fractions show a part of something using two numbers (numerator/denominator).
  
• Decimals use base-10 notation to show parts of one whole.
  
• Percents express parts out of 100.
  

This relationship lets us switch between them to better understand numbers in different formats.

Converting Fractions to Decimals

How do you convert a fraction into a decimal?

To convert a fraction to a decimal:

• Divide the numerator by the denominator.
  

Example:
1120=11÷20=0.55\frac{11}{20} = 11 ÷ 20 = 0.552011​=11÷20=0.55
(from quiz Question 7)​

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Practice Table: Common Conversions

Student Thought: Why divide? Because division shows how many times the denominator fits into the numerator, telling us the decimal part of a whole.

Converting Decimals to Percents

What steps help convert decimals into percents easily?

To convert a decimal into a percent:

• Multiply the decimal by 100
  
• Add a % sign
  

Shortcut: Move the decimal two places to the right.

Example:

• 0.56=56%0.56 = 56\%0.56=56% (from quiz Question 1)​
  
• 0.37=37%0.37 = 37\%0.37=37% (from quiz Question 2)
  

Table: Decimal to Percent Conversions

Quick Check: Why does multiplying by 100 work? Because percent means "per hundred."

Converting Percents to Decimals

What is the reverse of converting decimals to percents?

To go from percent to decimal:

• Divide the percent by 100
  
• Move the decimal two places to the left
  

Example:

• 50%=50÷100=0.5050\% = 50 ÷ 100 = 0.5050%=50÷100=0.50 (from quiz Question 3)​
  
• 3%=0.033\% = 0.033%=0.03 (from quiz Question 4)
  

Converting Percents to Fractions

Can you write a percent as a fraction?

Yes! To convert a percent to a fraction:

1. Put the percent over 100 (since "percent" means per 100)
   
2. Simplify the fraction
   

Example:

• 5%=5100=1205\% = \frac{5}{100} = \frac{1}{20}5%=1005​=201​
  
• 99%=9910099\% = \frac{99}{100}99%=10099​ (from quiz Questions 5 and 6)​
  

Converting Fractions to Percents (Using Decimals)

What if a fraction needs to be turned into a percent?

Use a two-step method:

1. Convert the fraction to a decimal by dividing.
   
2. Convert that decimal to a percent by multiplying by 100.
   

Example:

• 920=9÷20=0.45→0.45×100=45%\frac{9}{20} = 9 ÷ 20 = 0.45 → 0.45 × 100 = 45\%209​=9÷20=0.45→0.45×100=45%
  (from quiz Question 9)​
  

Example:

• 1100=0.01→1%\frac{1}{100} = 0.01 → 1\%1001​=0.01→1%
  (from quiz Question 10)​
  

All Conversions

Thought-Provoking Practice Questions

• Why is 0.99 equal to 99% but not 0.099?
  
• Is 1/4 the same as 25%? Try converting it to decimal and percent.
  
• Can two different fractions have the same decimal or percent value? Try 2/4 and 1/2.
  

Common Mistakes to Avoid

• Confusing decimal place movement: Moving right for decimals to percents, but left for percents to decimals.
  
• Incorrect division: For example, 2 ÷ 25 = 0.08, not 1.25.
  
• Not simplifying fractions: Always reduce where possible to recognize familiar values.
  

Real-World Connection

• Shopping: A 25% discount is the same as paying 75% of the price.
  
• Weather: 70% chance of rain means 0.7 probability.
  
• Sports: A batting average of 0.33 means 33% hit rate.
  

Understanding these conversions is crucial to interpreting numbers you see every day.

Key Takeaway

By mastering Converting Fractions to Decimal Numbers to Percents, you're unlocking a powerful math skill used in school and life. Whether calculating discounts or understanding data, you now know how to confidently switch between formats.

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