Converting Decimals to Fractions

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

Intermediate20 minLesson

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!

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What is as a fraction in lowest terms?

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:

Interactive Visual

Place Value Chart

Enter a number:

0.75

Ones 1	Tenths 0.1	Hundredths 0.01
0	7	5

Expanded Form:

7 × 0.1 + 5 × 0.01

Click on any place value to highlight it and see its value.

Numerator:

Denominator:

3/4

Click on the circle to change the fraction

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

17 problems

Problem 1 of 17

Easy

What is as a fraction in lowest terms?

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

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

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