Decimal to Fraction Lesson: Learn the Conversion

Lesson Overview

• What Is a Decimal?
• What Is a Fraction?
• How to Convert a Decimal to a Fraction
• Converting Tenths and Hundredths
• Converting Thousands and Beyond
• Decimals with Whole Numbers (Mixed Numbers)
• Practice with Four-Place Decimals
• How to Simplify Fractions
• Special Case: Repeating Decimals
• More Practice Examples

In math, numbers can be written in different forms: whole numbers, fractions, and decimals. Decimals and fractions are especially useful when dealing with parts of a whole. They might look different, but they often represent the same value.

This lesson will help you understand how to convert decimals into fractions, simplify them, and recognize what each part means. You'll learn how to handle both simple decimals and more detailed ones, including decimals with four or five digits after the point. You'll also learn the rules that help make fractions easier to work with.

What Is a Decimal?

A decimal is a way of writing a number that is less than one or between whole numbers. It uses a decimal point to separate the whole number part from the fractional part.

Example:

• 0.5 means 5 tenths
  
• 2.75 means 2 whole and 75 hundredths
  

Each digit after the decimal point has a place value:

Understanding these place values is important because they tell us what denominator to use when writing the decimal as a fraction.

What Is a Fraction?

A fraction shows a part of a whole. It has two parts:

• Numerator: The top number, showing how many parts we have
  
• Denominator: The bottom number, showing the total number of equal parts
  

Example:
In 3/4, we have 3 out of 4 parts.

When converting decimals to fractions, we're simply writing that same part in a different form.

How to Convert a Decimal to a Fraction

Follow these four steps:

1. Count how many digits are after the decimal point.
   
2. Write the decimal as a fraction, using the correct power of ten as the denominator.
   
3. Remove the decimal point and write the number as the numerator.
   
4. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF).
   

Let's practice!

Take This Quiz:

Fractions and Decimals Quiz! Test

Converting Tenths and Hundredths

Example 1: Convert 0.6 to a fraction

• There is 1 digit after the decimal → use 10 as the denominator
  
• 0.6 = 6/10
  
• Simplify: 6 ÷ 2 = 3, 10 ÷ 2 = 5
  Answer: 3/5
  

Example 2: Convert 0.16 to a fraction

• There are 2 digits → use 100 as the denominator
  
• 0.16 = 16/100
  
• Simplify: 16 ÷ 4 = 4, 100 ÷ 4 = 25
  Answer: 4/25
  

Converting Thousands and Beyond

Example 3: Convert 0.625 to a fraction

• Three digits after the decimal → denominator = 1000
  
• 0.625 = 625/1000
  
• Find GCF of 625 and 1000 → it's 125
  
• Simplify: 625 ÷ 125 = 5, 1000 ÷ 125 = 8
  Answer: 5/8
  

Example 4: Convert 0.84375 to a fraction

• 5 digits → denominator = 100000
  
• 0.84375 = 84375/100000
  
• GCF = 3125 → Simplify:
  84375 ÷ 3125 = 27
  100000 ÷ 3125 = 32
  Answer: 27/32
  

Decimals with Whole Numbers (Mixed Numbers)

When a decimal has a whole number and a decimal part, convert only the decimal part to a fraction, then combine it with the whole number.

Example 5: Convert 7.125 to a fraction

Step 1: Whole number = 7
Step 2: Decimal part = 0.125 = 1/8
Step 3: Combine: 7 + 1/8 = 57/8

To convert to an improper fraction:

• Multiply 7 × 8 = 56
  
• Add the numerator: 56 + 1 = 57
  
• Use the same denominator → 57/8
  

Practice with Four-Place Decimals

Example 6: Convert 0.6875 to a fraction

• 4 digits after the decimal → denominator = 10,000
  
• 0.6875 = 6875/10000
  
• GCF = 625
  6875 ÷ 625 = 11
  10000 ÷ 625 = 16
  Answer: 11/16
  

Take This Quiz:

Fractions And Decimals Practice Questions!

How to Simplify Fractions

Simplifying means making a fraction as small as possible by dividing the numerator and denominator by the same number.

Example: Simplify 18/24

• Find the greatest number that divides both 18 and 24. That's 6
  
• 18 ÷ 6 = 3, 24 ÷ 6 = 4
  Answer: 3/4
  

You can always simplify fractions after converting from decimals to make them easier to use.

Special Case: Repeating Decimals

Sometimes, a decimal goes on forever, like 0.333... or 0.666... These are called repeating decimals.

You won't usually convert these unless you're working with:

• 0.333... = 1/3
  
• 0.666... = 2/3
  

These conversions use algebraic tricks beyond Grade 5, so we focus more on terminating decimals (those that stop).

Take This Quiz:

Can You Pass This Decimal To Fraction Quiz?

More Practice Examples

Let's try more examples step-by-step.

Example 7: Convert 0.5625 to a fraction

• Decimal = 0.5625 → 5625/10000
  
• GCF = 625
  5625 ÷ 625 = 9
  10000 ÷ 625 = 16
  Answer: 9/16
  

Example 8: Convert 27.375 to a fraction

Step 1: Decimal part = 0.375 = 3/8
Step 2: Whole number = 27
27 × 8 = 216
216 + 3 = 219
Answer: 219/8