Have you ever come across a math problem and wondered how to change a fraction into a decimal or a decimal into a fraction and you couldn’t understand how to do it?
We have good news for you: it’s easier than you think!
In this tutorial, you’ll learn:
- What fractions and decimals are
- How to convert between them (in both directions)
- A few shortcuts and tips to save time
- Common mistakes to avoid
Let’s break it down together!
Also Read: Understanding Fractions Made Easy
What Is a Fraction and What Is a Decimal?
A fraction is a part of a whole (example value or number) and is written as:
numerator / denominator (for example, it is written as: ½, ¾, 5/8)
A decimal is another way to show a part of a whole (example value or number) using a decimal point:
(for example, it is written as: 0.5, 0.75, 0.625)
Though both fraction and decimal represent the same thing, just that they are written in different formats.
How to Convert Fractions to Decimals
Method 1: Divide the Numerator by the Denominator
To convert a fraction to a decimal, this is how you will do it:
Divide the top number (called, numerator) by the bottom number (also called, denominator)
Example 1:
1/2 = 1 ÷ 2 = 0.5
Example 2:
3/4 = 3 ÷ 4 = 0.75
Example 3:
5/8 = 5 ÷ 8 = 0.625
You can use a calculator or long division!
Quick Tip:
Some common fractions have decimals that repeat:
- 1/3 = 0.333… (repeating 3)
- 2/3 = 0.666…
- 1/6 = 0.1666…
Use a bar notation for repeating decimals:
1/3 = 0.3̅
How to Convert Decimals to Fractions
Step-by-Step Method:
- Count the decimal places (how many digits after the point)
- Write the decimal as a fraction with a denominator of 10, 100, or 1000 depending on the digits
- Simplify the fraction
Example 1:
ini
0.5 = 5/10 → Simplify → ½
Example 2:
ini
0.75 = 75/100 → Simplify → 3/4
Example 3:
ini
0.125 = 125/1000 → Simplify → 1/8
A Quick Trick:
If the decimal terminates (ends), just use place value:
- 0.2 = 2/10 = 1/5
- 0.6 = 6/10 = 3/5
- 0.04 = 4/100 = 1/25
Handy Conversion Chart
Fraction Decimal
1/2 0.5
1/3 0.333…
1/4 0.25
3/4 0.75
1/5 0.2
2/5 0.4
1/8 0.125
5/8 0.625
You can print or memorize this chart for quick reference.
Common Mistakes to Avoid
Forgetting to simplify fractions
Using the wrong number of zeros when converting decimals
Ignoring repeating decimals
Trying to convert by estimation only (use division for accuracy)
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Practice Problems
Convert These Fractions to Decimals:
- 1/4 = ?
- 7/10 = ?
- 3/8 = ?
Answers:
- 0.25
- 0.7
- 0.375
Convert These Decimals to Fractions:
- 0.6 = ?
- 0.125 = ?
- 0.2 = ?
Answers:
- 3/5
- 1/8
- 1/5
Summary
- To convert fractions to decimals: Divide the numerator by the denominator
- To convert decimals to fractions: Use place value and simplify
- Remember common conversions and practice regularly
Action
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