Teacher Guide: Converting Decimals to Fractions

Learn how to convert any decimal number into a fraction and simplify it to lowest terms.

Present LessonView Student Page

Use this lesson with your class

Free, no student accounts needed.

Share with students

Students open the lesson and practise with instant feedback.

Printable worksheet

All practice problems on paper, with a separate answer key.

Worksheet Answer key

Class quiz

10 questions on Conversions. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives

Convert terminating decimals to fractions using place value
Simplify fractions to lowest terms using the GCF
Convert decimals greater than 1 to mixed numbers
Apply decimal-to-fraction conversion in real-world contexts

Prerequisites

• Understanding decimal place values (tenths, hundredths, thousandths)
• Basic understanding of fractions
• Finding the greatest common factor (GCF)

Discussion Starters

1. Why might someone prefer using fractions instead of decimals?
2. Can you think of situations where decimals are easier to use than fractions?
3. How would you explain the conversion process to a younger student?
4. What patterns do you notice when converting common decimals like , , and ?

Common Misconceptions

Thinking equals because both have a 5

Believing all decimals can be written as fractions with small denominators

Differentiation Ideas

For Struggling Students:

• Start with only tenths (one decimal place)
• Provide a place value chart as a reference
• Use visual fraction models to verify answers

For On-Level Students:

• Practice with tenths, hundredths, and thousandths
• Include mixed numbers (decimals greater than 1)
• Focus on simplifying to lowest terms

For Advanced Students:

• Explore patterns with repeating decimals
• Convert back and forth between forms
• Challenge: Which fractions produce terminating vs repeating decimals?

Standards Alignment

6.NS.C.6.C (CCSS.MATH.CONTENT.6.NS.C.6.C)
Find and position integers and other rational numbers on a horizontal or vertical number line diagram
7.NS.A.2.D (CCSS.MATH.CONTENT.7.NS.A.2.D)
Convert a rational number to a decimal using long division

Lesson Resources

visualPlace Value Chart
Interactive chart showing decimal place values
activityDecimal-Fraction Matching
Match decimals with their equivalent fractions
worksheetConversion Practice
Practice problems with varying difficulty

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

To convert a decimal to a fraction, use the place value of the last digit:

1. Write the decimal as a fraction with the appropriate power of 10 as the denominator 2. Simplify the fraction to lowest terms

Decimal	Place Value	Fraction	Simplified
	Tenths
	Hundredths
	Thousandths

Key insight: The number of decimal places tells you how many zeros to put in the denominator!

Worked Examples

Convert to a fraction.

Identify the place value

The 4 is in the tenths place → Denominator will be

Write as a fraction

→

Find the GCF

GCF of and is → GCF

Simplify

→

Answer:

Common Mistakes

Using the wrong denominator (e.g., writing as )

Why it's wrong: The denominator depends on the place value of the LAST digit. In , the 5 is in the hundredths place, not tenths.

Correct: Count the decimal places: 2 places = 100, so

Forgetting to simplify the fraction

Why it's wrong: While is technically correct, fractions should be in lowest terms.

Correct: Always check if the numerator and denominator share common factors.

Dropping leading zeros in the numerator

Why it's wrong: For , writing instead of gives the wrong value.

Correct: has 2 decimal places, so:

Why It Matters

Converting between decimals and fractions is essential in everyday life:

Cooking: A recipe calls for cups of flour - that's cup!
Money: 50 cents is or of a dollar
Measurements: A carpenter measures inches, which equals inch
Discounts: A 25% discount () means you pay of the original price

Fractions are often easier to visualize and work with than decimals!

Real World Applications

Cooking and Recipes

Many measuring cups show both decimal and fraction measurements.

Example:

If a digital scale shows kg of flour, that equals kg.

1Try It Yourself

A recipe calls for cups of sugar.

What fraction of a cup is this?

Step 1: Write the mathematical expression

Convert to a fraction:

Shopping Discounts

Sales often show discounts as decimals that are easier to understand as fractions.

Example:

A discount means you save of the price.

2Try It Yourself

A store offers a discount on all items.

What fraction of the price do you save?

Step 1: Write the mathematical expression

Convert to a fraction:

Key Takeaways

1To convert a decimal to a fraction, use the place value of the last digit as the denominator
2Count decimal places: 1 place = 10, 2 places = 100, 3 places = 1000
3Always simplify the fraction by dividing by the GCF
4For decimals greater than 1, handle the whole number and decimal parts separately

Frequently Asked Questions

How do I convert a repeating decimal like to a fraction?

Repeating decimals require a different method. For , this equals . In general, for a single repeating digit, put it over 9: .

Why does the number of decimal places matter?

Each decimal place represents a power of 10. Tenths = 10, hundredths = 100, thousandths = 1000. The position tells you the denominator.

What if my fraction doesn't simplify?

Some fractions are already in lowest terms. For example, cannot be simplified because 17 is prime and doesn't divide 100.

Glossary

Decimal: A number written using place value and a decimal point (e.g., )
Fraction: A number written as one integer divided by another (e.g., )
Place value: The value of a digit based on its position (tenths, hundredths, thousandths)
Simplify: To reduce a fraction to lowest terms by dividing by the GCF
GCF: Greatest Common Factor - the largest number that divides both numbers evenly

Formula Card

General Method

Convert any decimal to a fraction

Tenths

One decimal place

Hundredths

Two decimal places

Thousandths

Three decimal places